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In the first paper of this two part communication, we solved in a unified framework a variety of two terminal source coding problems with noncooperative encoders, thereby consolidating works of Shannon, Slepian-Wolf, Wyner, Ahlswede-K\"{o}rner, Wyner-Ziv, Berger {\em et al.} and Berger-Yeung. To achieve such unification we made use of a fundamental principle that dissociates bulk of the analysis from the distortion criterion at hand (if any) and extends the typicality arguments of Shannon and Wyner-Ziv. In this second paper, we generalize the fundamental principle for any number of sources and on its basis exhaustively solve all multiterminal source coding problems with noncooperative encoders and one decoder. The distortion criteria, when applicable, are required to apply to single letters and be bounded. Our analysis includes cases where side information is, respectively, partially available, completely available and altogether unavailable at the decoder. As seen in our first paper, the achievable regions permit infinite order information-theoretic descriptions. We also show that the entropy-constrained multiterminal estimation problem can be solved as a special case of our theory. | Unified Theory of Source Coding: Part II -- Multiterminal Problems | 7,000 |
This paper investigates the achievable information rate of phase-shift keying (PSK) over frequency non-selective Rayleigh fading channels without channel state information (CSI). The fading process exhibits general temporal correlation characterized by its spectral density function. We consider both discrete-time and continuous-time channels, and find their asymptotics at low signal-to-noise ratio (SNR). Compared to known capacity upper bounds under peak constraints, these asymptotics usually lead to negligible rate loss in the low-SNR regime for slowly time-varying fading channels. We further specialize to case studies of Gauss-Markov and Clarke's fading models. | How Good is Phase-Shift Keying for Peak-Limited Rayleigh Fading Channels
in the Low-SNR Regime? | 7,001 |
Motivated by the evident success of context-tree based methods in lossless data compression, we explore, in this paper, methods of the same spirit in universal prediction of individual sequences. By context-tree prediction, we refer to a family of prediction schemes, where at each time instant $t$, after having observed all outcomes of the data sequence $x_1,...,x_{t-1}$, but not yet $x_t$, the prediction is based on a ``context'' (or a state) that consists of the $k$ most recent past outcomes $x_{t-k},...,x_{t-1}$, where the choice of $k$ may depend on the contents of a possibly longer, though limited, portion of the observed past, $x_{t-k_{\max}},...x_{t-1}$. This is different from the study reported in [1], where general finite-state predictors as well as ``Markov'' (finite-memory) predictors of fixed order, were studied in the regime of individual sequences. Another important difference between this study and [1] is the asymptotic regime. While in [1], the resources of the predictor (i.e., the number of states or the memory size) were kept fixed regardless of the length $N$ of the data sequence, here we investigate situations where the number of contexts or states is allowed to grow concurrently with $N$. We are primarily interested in the following fundamental question: What is the critical growth rate of the number of contexts, below which the performance of the best context-tree predictor is still universally achievable, but above which it is not? We show that this critical growth rate is linear in $N$. In particular, we propose a universal context-tree algorithm that essentially achieves optimum performance as long as the growth rate is sublinear, and show that, on the other hand, this is impossible in the linear case. | On context-tree prediction of individual sequences | 7,002 |
In this paper, we complement Verd\'{u}'s work on spectral efficiency in the wideband regime by investigating the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both AWGN and Rayleigh-fading channels. For the AWGN channel model, the optimal values of $R_z(0)$ and $\dot{R_z}(0)$ are calculated, where $R_z(1/B)$ is the maximum rate at which information can be transmitted over a channel with bandwidth $B/2$ when the error-exponent is constrained to be greater than or equal to $z.$ Based on this calculation, we say that a sequence of input distributions is near optimal if both $R_z(0)$ and $\dot{R_z}(0)$ are achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full CSI is available at the receiver. | Asymptotic Behavior of Error Exponents in the Wideband Regime | 7,003 |
In this work, we extend the non-orthogonal amplify-and-forward (NAF) cooperative diversity scheme to the MIMO channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the non-vanishing determinant criterion (NVD) and is shown to achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. We provide a general explicit algebraic construction, followed by some examples. In particular, in the single relay case, it is proved that the Golden code and the 4x4 Perfect code are optimal for the single-antenna and two-antenna case, respectively. Simulation results reveal that a significant gain (up to 10dB) can be obtained with the proposed codes, especially in the single-antenna case. | Optimal space-time codes for the MIMO amplify-and-forward cooperative
channel | 7,004 |
Non-data-aided (NDA) parameter estimation is considered for binary-phase-shift-keying transmission in an additive white Gaussian noise channel. Cramer-Rao lower bounds (CRLBs) for signal amplitude, noise variance, channel reliability constant and bit-error rate are derived and it is shown how these parameters relate to the signal-to-noise ratio (SNR). An alternative derivation of the iterative maximum likelihood (ML) SNR estimator is presented together with a novel, low complexity NDA SNR estimator. The performance of the proposed estimator is compared to previously suggested estimators and the CRLB. The results show that the proposed estimator performs close to the iterative ML estimator at significantly lower computational complexity. | Non-Data-Aided Parameter Estimation in an Additive White Gaussian Noise
Channel | 7,005 |
An algorithm that performs joint equalization and decoding for nonlinear two-dimensional intersymbol interference channels is presented. The algorithm performs sum-product message-passing on a factor graph that represents the underlying system. The two-dimensional optical storage (TWODOS) technology is an example of a system with nonlinear two-dimensional intersymbol interference. Simulations for the nonlinear channel model of TWODOS show significant improvement in performance over uncoded performance. Noise tolerance thresholds for the algorithm for the TWODOS channel, computed using density evolution, are also presented and accurately predict the limiting performance of the algorithm as the codeword length increases. | Joint Equalization and Decoding for Nonlinear Two-Dimensional
Intersymbol Interference Channels with Application to Optical Storage | 7,006 |
An algorithm that performs joint equalization and decoding for channels with nonlinear two-dimensional intersymbol interference is presented. The algorithm performs sum-product message-passing on a factor graph that represents the underlying system. The two-dimensional optical storage (TwoDOS) technology is an example of a system with nonlinear two-dimensional intersymbol interference. Simulations for the nonlinear channel model of TwoDOS show significant improvement in performance over uncoded performance. Noise tolerance thresholds for the TwoDOS channel computed using density evolution are also presented. | Joint Equalization and Decoding for Nonlinear Two-Dimensional
Intersymbol Interference Channels | 7,007 |
Joint equalization and decoding schemes are described for two-dimensional intersymbol interference (ISI) channels. Equalization is performed using the minimum mean-square-error (MMSE) criterion. Low-density parity-check codes are used for error correction. The MMSE schemes are the extension of those proposed by Tuechler et al. (2002) for one-dimensional ISI channels. Extrinsic information transfer charts, density evolution, and bit-error rate versus signal-to-noise ratio curves are used to study the performance of the schemes. | Minimum Mean-Square-Error Equalization using Priors for Two-Dimensional
Intersymbol Interference | 7,008 |
Density evolution is one of the most powerful analytical tools for low-density parity-check (LDPC) codes and graph codes with message passing decoding algorithms. With channel symmetry as one of its fundamental assumptions, density evolution (DE) has been widely and successfully applied to different channels, including binary erasure channels, binary symmetric channels, binary additive white Gaussian noise channels, etc. This paper generalizes density evolution for non-symmetric memoryless channels, which in turn broadens the applications to general memoryless channels, e.g. z-channels, composite white Gaussian noise channels, etc. The central theorem underpinning this generalization is the convergence to perfect projection for any fixed size supporting tree. A new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed. Several properties of the new density evolution method are explored, including stability results for general asymmetric memoryless channels. Simulations, code optimizations, and possible new applications suggested by this new density evolution method are also provided. This result is also used to prove the typicality of linear LDPC codes among the coset code ensemble when the minimum check node degree is sufficiently large. It is shown that the convergence to perfect projection is essential to the belief propagation algorithm even when only symmetric channels are considered. Hence the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels. | Density Evolution for Asymmetric Memoryless Channels | 7,009 |
In this paper, an outage limited MIMO channel is considered. We build on Zheng and Tse's elegant formulation of the diversity-multiplexing tradeoff to develop a better understanding of the asymptotic relationship between the probability of error, transmission rate, and signal-to-noise ratio. In particular, we identify the limitation imposed by the multiplexing gain notion and develop a new formulation for the throughput-reliability tradeoff that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of MIMO channels. | The Throughput-Reliability Tradeoff in MIMO Channels | 7,010 |
We consider both channel coding and source coding, with perfect past feedback/feedforward, in the presence of side information. It is first observed that feedback does not increase the capacity of the Gel'fand-Pinsker channel, nor does feedforward improve the achievable rate-distortion performance in the Wyner-Ziv problem. We then focus on the Gaussian case showing that, as in the absence of side information, feedback/feedforward allows to efficiently attain the respective performance limits. In particular, we derive schemes via variations on that of Schalkwijk and Kailath. These variants, which are as simple as their origins and require no binning, are shown to achieve, respectively, the capacity of Costa's channel, and the Wyner-Ziv rate distortion function. Finally, we consider the finite-alphabet setting and derive schemes for both the channel and the source coding problems that attain the fundamental limits, using variations on schemes of Ahlswede and Ooi and Wornell, and of Martinian and Wornell, respectively. | Coding for the feedback Gel'fand-Pinsker channel and the feedforward
Wyner-Ziv source | 7,011 |
This paper investigates an efficient and practical information reconciliation method in the case where two parties have access to correlated continuous random variables. We show that reconciliation is a special case of channel coding and that existing coded modulation techniques can be adapted for reconciliation. We describe an explicit reconciliation method based on LDPC codes in the case of correlated Gaussian variables. We believe that the proposed method can improve the efficiency of quantum key distribution protocols based on continuous-spectrum quantum states. | Efficient Reconciliation of Correlated Continuous Random Variables using
LDPC Codes | 7,012 |
In this paper, we define the power region as the set of power allocations for K users such that everybody meets a minimum signal-to-interference ratio (SIR). The SIR is modeled in a multiuser CDMA system with fixed linear receiver and signature sequences. We show that the power region is convex in linear and logarithmic scale. It furthermore has a componentwise minimal element. Power constraints are included by the intersection with the set of all viable power adjustments. In this framework, we aim at minimizing the total expended power by minimizing a componentwise monotone functional. If the feasible power region is nonempty, the minimum is attained. Otherwise, as a solution to balance conflicting interests, we suggest the projection of the minimum point in the power region onto the set of viable power settings. Finally, with an appropriate utility function, the problem of minimizing the total expended power can be seen as finding the Nash bargaining solution, which sheds light on power assignment from a game theoretic point of view. Convexity and componentwise monotonicity are essential prerequisites for this result. | Optimal Power Control for Multiuser CDMA Channels | 7,013 |
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity} per information bit. It also introduces symmetry properties which play a central role in the construction of capacity-achieving ensembles for the BEC. The results here improve on the tradeoff between performance and complexity provided by the first capacity-achieving ensembles of irregular repeat-accumulate (IRA) codes with bounded complexity per information bit; these IRA ensembles were previously constructed by Pfister, Sason and Urbanke. The superiority of ARA codes with moderate to large block length is exemplified by computer simulations which compare their performance with those of previously reported capacity-achieving ensembles of LDPC and IRA codes. The ARA codes also have the advantage of being systematic. | Accumulate-Repeat-Accumulate Codes: Systematic Codes Achieving the
Binary Erasure Channel Capacity with Bounded Complexity | 7,014 |
We study a game puzzle that has enjoyed recent popularity among mathematicians, computer scientist, coding theorists and even the mass press. In the game, $n$ players are fitted with randomly assigned colored hats. Individual players can see their teammates' hat colors, but not their own. Based on this information, and without any further communication, each player must attempt to guess his hat color, or pass. The team wins if there is at least one correct guess, and no incorrect ones. The goal is to devise guessing strategies that maximize the team winning probability. We show that for the case of two hat colors, and for any value of $n$, playing strategies are equivalent to binary covering codes of radius one. This link, in particular with Hamming codes, had been observed for values of $n$ of the form $2^m-1$. We extend the analysis to games with hats of $q$ colors, $q\geq 2$, where 1-coverings are not sufficient to characterize the best strategies. Instead, we introduce the more appropriate notion of a {\em strong covering}, and show efficient constructions of these coverings, which achieve winning probabilities approaching unity. Finally, we briefly discuss results on variants of the problem, including arbitrary input distributions, randomized playing strategies, and symmetric strategies. | On Hats and other Covers | 7,015 |
An interference-limited noise-free CDMA downlink channel operating under a complexity constraint on the receiver is introduced. According to this paradigm, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. This channel setting, allowing the use of the simplest receiver scheme, seems to be worthless, making reliable communication at any rate impossible. We prove, by adopting statistical mechanics notion, that in the large-system limit such a complexity-constrained CDMA channel gives rise to a non-trivial Shannon-theoretic capacity, rigorously analyzed and corroborated using finite-size channel simulations. | Capacity of Complexity-Constrained Noise-Free CDMA | 7,016 |
A noisy CDMA downlink channel operating under a strict complexity constraint on the receiver is introduced. According to this constraint, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. This channel setting, allowing the use of the simplest receiver scheme, seems to be worthless, making reliable communication at any rate impossible. However, recently this communication paradigm was shown to yield valuable information rates in the case of a noiseless channel. This finding calls for the investigation of this attractive complexity-constrained transmission scheme for the more practical noisy channel case. By adopting the statistical mechanics notion of metastable states of the renowned Hopfield model, it is proved that under a bounded noise assumption such complexity-constrained CDMA channel gives rise to a non-trivial Shannon-theoretic capacity, rigorously analyzed and corroborated using finite-size channel simulations. For unbounded noise the channel's outage capacity is addressed and specifically described for the popular additive white Gaussian noise. | On the Achievable Information Rates of CDMA Downlink with Trivial
Receivers | 7,017 |
We introduce a new family of concatenated codes with an outer low-density parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code, and prove that these codes can achieve capacity under any memoryless binary-input output-symmetric (MBIOS) channel using maximum-likelihood (ML) decoding with bounded graphical complexity, i.e., the number of edges per information bit in their graphical representation is bounded. In particular, we also show that these codes can achieve capacity on the binary erasure channel (BEC) under belief propagation (BP) decoding with bounded decoding complexity per information bit per iteration for all erasure probabilities in (0, 1). By deriving and analyzing the average weight distribution (AWD) and the corresponding asymptotic growth rate of these codes with a rate-1 inner LDGM code, we also show that these codes achieve the Gilbert-Varshamov bound with asymptotically high probability. This result can be attributed to the presence of the inner rate-1 LDGM code, which is demonstrated to help eliminate high weight codewords in the LDPC code while maintaining a vanishingly small amount of low weight codewords. | Capacity-Achieving Codes with Bounded Graphical Complexity on Noisy
Channels | 7,018 |
For generalized Reed-Solomon codes, it has been proved \cite{GuruswamiVa05} that the problem of determining if a received word is a deep hole is co-NP-complete. The reduction relies on the fact that the evaluation set of the code can be exponential in the length of the code -- a property that practical codes do not usually possess. In this paper, we first presented a much simpler proof of the same result. We then consider the problem for standard Reed-Solomon codes, i.e. the evaluation set consists of all the nonzero elements in the field. We reduce the problem of identifying deep holes to deciding whether an absolutely irreducible hypersurface over a finite field contains a rational point whose coordinates are pairwise distinct and nonzero. By applying Schmidt and Cafure-Matera estimation of rational points on algebraic varieties, we prove that the received vector $(f(\alpha))_{\alpha \in \F_q}$ for Reed-Solomon $[q,k]_q$, $k < q^{1/7 - \epsilon}$, cannot be a deep hole, whenever $f(x)$ is a polynomial of degree $k+d$ for $1\leq d < q^{3/13 -\epsilon}$. | On Deciding Deep Holes of Reed-Solomon Codes | 7,019 |
Wide band systems operating over multipath channels may spread their power over bandwidth if they use duty cycle. Channel uncertainty limits the achievable data rates of power constrained wide band systems; Duty cycle transmission reduces the channel uncertainty because the receiver has to estimate the channel only when transmission takes place. The optimal choice of the fraction of time used for transmission depends on the spectral efficiency of the signal modulation. The general principle is demonstrated by comparing the channel conditions that allow different modulations to achieve the capacity in the limit. Direct sequence spread spectrum and pulse position modulation systems with duty cycle achieve the channel capacity, if the increase of the number of channel paths with the bandwidth is not too rapid. The higher spectral efficiency of the spread spectrum modulation lets it achieve the channel capacity in the limit, in environments where pulse position modulation with non-vanishing symbol time cannot be used because of the large number of channel paths. | Channel Uncertainty in Ultra Wideband Communication Systems | 7,020 |
In this paper, we analyze the capacity of multiple-input multiple-output (MIMO) Rayleigh-fading channels in the presence of spatial fading correlation at both the transmitter and the receiver, assuming that the channel is unknown at the transmitter and perfectly known at the receiver. We first derive the determinant representation for the exact characteristic function of the capacity, which is then used to determine the trace representations for the mean, variance, skewness, kurtosis, and other higher-order statistics (HOS). These results allow us to exactly evaluate two relevant information-theoretic capacity measures--ergodic capacity and outage capacity--and the HOS of the capacity for such a MIMO channel. The analytical framework presented in the paper is valid for arbitrary numbers of antennas and generalizes the previously known results for independent and identically distributed or one-sided correlated MIMO channels to the case when fading correlation exists on both sides. We verify our analytical results by comparing them with Monte Carlo simulations for a correlation model based on realistic channel measurements as well as a classical exponential correlation model. | On the Capacity of Doubly Correlated MIMO Channels | 7,021 |
We investigate the capacity of opportunistic communication in the presence of dynamic and distributed spectral activity, i.e. when the time varying spectral holes sensed by the cognitive transmitter are correlated but not identical to those sensed by the cognitive receiver. Using the information theoretic framework of communication with causal and non-causal side information at the transmitter and/or the receiver, we obtain analytical capacity expressions and the corresponding numerical results. We find that cognitive radio communication is robust to dynamic spectral environments even when the communication occurs in bursts of only 3-5 symbols. The value of handshake overhead is investigated for both lightly loaded and heavily loaded systems. We find that the capacity benefits of overhead information flow from the transmitter to the receiver is negligible while feedback information overhead in the opposite direction significantly improves capacity. | Capacity Limits of Cognitive Radio with Distributed and Dynamic Spectral
Activity | 7,022 |
The capacity of stationary additive Gaussian noise channels with feedback is characterized as the solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. When specialized to the first-order autoregressive moving-average noise spectrum, this variational characterization yields a closed-form expression for the feedback capacity. In particular, this result shows that the celebrated Schalkwijk--Kailath coding scheme achieves the feedback capacity for the first-order autoregressive moving-average Gaussian channel, resolving a long-standing open problem studied by Butman, Schalkwijk--Tiernan, Wolfowitz, Ozarow, Ordentlich, Yang--Kavcic--Tatikonda, and others. | On the Feedback Capacity of Stationary Gaussian Channels | 7,023 |
Optimal link adaption to the scattering function of wide sense stationary uncorrelated mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission such link adaption is performed by pulse shaping, i.e. by properly adjusting the transmit and receive filters. For example pulse shaped Offset--QAM systems have been recently shown to have superior performance over standard cyclic prefix OFDM (while operating at higher spectral efficiency).In this paper we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so-called Weyl--Heisenberg or Gabor signaling with respect to the scattering function of the WSSUS channel. In our framework the pulse shape optimization problem is translated to an optimization problem over trace class operators which in turn is related to fidelity optimization in quantum information processing. By convexity relaxation the problem is shown to be equivalent to a \emph{convex constraint quasi-convex maximization problem} thereby revealing the non-convex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization providing applicable results even for large--scale problem constellations. We show that with transmitter-side knowledge of the channel statistics a gain of $3 - 6$dB in $\SINR$ can be expected. | The WSSUS Pulse Design Problem in Multicarrier Transmission | 7,024 |
The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the perceptron-based code saturates the theoretically achievable limit in most cases although exactly performing the compression is computationally difficult. To resolve this difficulty, we provide a computationally tractable approximation algorithm using belief propagation (BP), which is a current standard algorithm of probabilistic inference. Introducing several approximations and heuristics, the BP-based algorithm exhibits performance that is close to the achievable limit in a practical time scale in optimal cases. | Statistical Mechanical Approach to Lossy Data Compression:Theory and
Practice | 7,025 |
Phase noise and frequency offsets are due to their time-variant behavior one of the most limiting disturbances in practical OFDM designs and therefore intensively studied by many authors. In this paper we present a generalized framework for the prediction of uncoded system performance in the presence of time-variant distortions including the transmitter and receiver pulse shapes as well as the channel. Therefore, unlike existing studies, our approach can be employed for more general multicarrier schemes. To show the usefulness of our approach, we apply the results to OFDM in the context of frequency offset and Wiener phase noise, yielding improved bounds on the uncoded performance. In particular, we obtain exact formulas for the averaged performance in AWGN and time-invariant multipath channels. | On Time-Variant Distortions in Multicarrier Transmission with
Application to Frequency Offsets and Phase Noise | 7,026 |
The use of multi-antenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated channels. Here, an approach is presented that provides analytic expressions not only for the average, but also the higher cumulant moments of the distribution of the mutual information for zero-mean Gaussian (multiple-input multiple-output) MIMO channels with the most general multipath covariance matrices when the channel is known at the receiver. These channels include multi-tap delay paths, as well as general channels with covariance matrices that cannot be written as a Kronecker product, such as dual-polarized antenna arrays with general correlations at both transmitter and receiver ends. The mathematical methods are formally valid for large antenna numbers, in which limit it is shown that all higher cumulant moments of the distribution, other than the first two scale to zero. Thus, it is confirmed that the distribution of the mutual information tends to a Gaussian, which enables one to calculate the outage capacity. These results are quite accurate even in the case of a few antennas, which makes this approach applicable to realistic situations. | On the Outage Capacity of Correlated Multiple-Path MIMO Channels | 7,027 |
In this paper, we analyze the frequency-hopping orthogonal frequency-division multiplexing (OFDM) system known as Multiband OFDM for high-rate wireless personal area networks (WPANs) based on ultra-wideband (UWB) transmission. Besides considering the standard, we also propose and study system performance enhancements through the application of Turbo and Repeat-Accumulate (RA) codes, as well as OFDM bit-loading. Our methodology consists of (a) a study of the channel model developed under IEEE 802.15 for UWB from a frequency-domain perspective suited for OFDM transmission, (b) development and quantification of appropriate information-theoretic performance measures, (c) comparison of these measures with simulation results for the Multiband OFDM standard proposal as well as our proposed extensions, and (d) the consideration of the influence of practical, imperfect channel estimation on the performance. We find that the current Multiband OFDM standard sufficiently exploits the frequency selectivity of the UWB channel, and that the system performs in the vicinity of the channel cutoff rate. Turbo codes and a reduced-complexity clustered bit-loading algorithm improve the system power efficiency by over 6 dB at a data rate of 480 Mbps. | Performance Analysis and Enhancement of Multiband OFDM for UWB
Communications | 7,028 |
In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of Reed-Solomon codes. | Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes | 7,029 |
We explore the SNR-optimal relay functionality in a \emph{memoryless} relay network, i.e. a network where, during each channel use, the signal transmitted by a relay depends only on the last received symbol at that relay. We develop a generalized notion of SNR for the class of memoryless relay functions. The solution to the generalized SNR optimization problem leads to the novel concept of minimum mean square uncorrelated error estimation(MMSUEE). For the elemental case of a single relay, we show that MMSUEE is the SNR-optimal memoryless relay function regardless of the source and relay transmit power, and the modulation scheme. This scheme, that we call estimate and forward (EF), is also shown to be SNR-optimal with PSK modulation in a parallel relay network. We demonstrate that EF performs better than the best of amplify and forward (AF) and demodulate and forward (DF), in both parallel and serial relay networks. We also determine that AF is near-optimal at low transmit power in a parallel network, while DF is near-optimal at high transmit power in a serial network. For hybrid networks that contain both serial and parallel elements, and when robust performance is desired, the advantage of EF over the best of AF and DF is found to be significant. Error probabilities are provided to substantiate the performance gain obtained through SNR optimality. We also show that, for \emph{Gaussian} inputs, AF, DF and EF become identical. | Optimal Relay Functionality for SNR Maximization in Memoryless Relay
Networks | 7,030 |
Linear space-time block codes (STBCs) of unitary rate and full diversity, systematically constructed over arbitrary constellations for any number of transmit antennas are introduced. The codes are obtained by generalizing the existing ABBA STBCs, a.k.a quasi-orthogonal STBCs (QO-STBCs). Furthermore, a fully orthogonal (symbol-by-symbol) decoder for the new generalized ABBA (GABBA) codes is provided. This remarkably low-complexity decoder relies on partition orthogonality properties of the code structure to decompose the received signal vector into lower-dimension tuples, each dependent only on certain subsets of the transmitted symbols. Orthogonal decodability results from the nested application of this technique, with no matrix inversion or iterative signal processing required. The exact bit-error-rate probability of GABBA codes over generalized fading channels with maximum likelihood (ML) decoding is evaluated analytically and compared against simulation results obtained with the proposed orthogonal decoder. The comparison reveals that the proposed GABBA solution, despite its very low complexity, achieves nearly the same performance of the bound corresponding to the ML-decoded system, especially in systems with large numbers of antennas. | Generalized ABBA Space-Time Block Codes | 7,031 |
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees $d=p^s$ and $d = p^s+1$, for $p$ a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for $p$-ary LDPC codes. Treating these codes as $p$-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes where $p > 2$. | Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights | 7,032 |
A unified approach to energy-efficient power control, applicable to a large family of receivers including the matched filter, the decorrelator, the (linear) minimum-mean-square-error detector (MMSE), and the individually and jointly optimal multiuser detectors, has recently been proposed for code-division-multiple-access (CDMA) networks. This unified power control (UPC) algorithm exploits the linear relationship that has been shown to exist between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) in large systems. Based on this principle and by computing the multiuser efficiency, the UPC algorithm updates the users' transmit powers in an iterative way to achieve the desired target SIR. In this paper, the convergence of the UPC algorithm is proved for the matched filter, the decorrelator, and the MMSE detector. In addition, the performance of the algorithm in finite-size systems is studied and compared with that of existing power control schemes. The UPC algorithm is particularly suitable for systems with randomly generated long spreading sequences (i.e., sequences whose period is longer than one symbol duration). | A Unified Power Control Algorithm for Multiuser Detectors in Large
Systems: Convergence and Performance | 7,033 |
In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on Semi-Definite Programming (SDP). We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models. The proposed relaxation models are also used for soft output decoding in MIMO systems. | A Near Maximum Likelihood Decoding Algorithm for MIMO Systems Based on
Semi-Definite Programming | 7,034 |
Suppose we have a signal y which we wish to represent using a linear combination of a number of basis atoms a_i, y=sum_i x_i a_i = Ax. The problem of finding the minimum L0 norm representation for y is a hard problem. The Basis Pursuit (BP) approach proposes to find the minimum L1 norm representation instead, which corresponds to a linear program (LP) that can be solved using modern LP techniques, and several recent authors have given conditions for the BP (minimum L1 norm) and sparse (minimum L0 solutions) representations to be identical. In this paper, we explore this sparse representation problem} using the geometry of convex polytopes, as recently introduced into the field by Donoho. By considering the dual LP we find that the so-called polar polytope P of the centrally-symmetric polytope P whose vertices are the atom pairs +-a_i is particularly helpful in providing us with geometrical insight into optimality conditions given by Fuchs and Tropp for non-unit-norm atom sets. In exploring this geometry we are able to tighten some of these earlier results, showing for example that the Fuchs condition is both necessary and sufficient for L1-unique-optimality, and that there are situations where Orthogonal Matching Pursuit (OMP) can eventually find all L1-unique-optimal solutions with m nonzeros even if ERC fails for m, if allowed to run for more than m steps. | Polar Polytopes and Recovery of Sparse Representations | 7,035 |
In this paper, we provide a performance analysis of a new class of serial concatenated convolutional codes (SCCC) where the inner encoder can be punctured beyond the unitary rate. The puncturing of the inner encoder is not limited to inner coded bits, but extended to systematic bits. Moreover, it is split into two different puncturings, in correspondence with inner code systematic bits and parity bits. We derive the analytical upper bounds to the error probability of this particular code structure and address suitable design guidelines for the inner code puncturing patterns. We show that the percentile of systematic and parity bits to be deleted strongly depends on the SNR region of interest. In particular, to lower the error floor it is advantageous to put more puncturing on inner systematic bits. Furthermore, we show that puncturing of inner systematic bits should be interleaver dependent. Based on these considerations, we derive design guidelines to obtain well-performing rate-compatible SCCC families. Throughout the paper, the performance of the proposed codes are compared with analytical bounds, and with the performance of PCCC and SCCC proposed in the literature. | Design and Performance Analysis of a New Class of Rate Compatible Serial
Concatenated Convolutional Codes | 7,036 |
This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship is used to quantify variation among the entities of a system, where variation is defined as tolerance, option, specification or implementation variation among the entities of a system. Variation has a significnt and increasing impact on communications system performance. This paper introduces means to identify, quantify and reduce such performance variations. | The "...system of constraints" | 7,037 |
We apply belief propagation (BP) to multi--user detection in a spread spectrum system, under the assumption of Gaussian symbols. We prove that BP is both convergent and allows to estimate the correct conditional expectation of the input symbols. It is therefore an optimal --minimum mean square error-- detection algorithm. This suggests the possibility of designing BP detection algorithms for more general systems. As a byproduct we rederive the Tse-Hanly formula for minimum mean square error without any recourse to random matrix theory. | Belief Propagation Based Multi--User Detection | 7,038 |
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity the various components in an iterative coding system have to be perfectly matched. This generalizes the perfect matching condition which was previously known for the case of transmission over the binary erasure channel to the general class of binary-input memoryless output-symmetric channels. Potential applications of this perfect matching condition are the construction of capacity-achieving degree distributions and the determination of the number required iterations as a function of the multiplicative gap to capacity. | Why We Can Not Surpass Capacity: The Matching Condition | 7,039 |
In this work, the geometric relation between space time block code design for the coherent channel and its non-coherent counterpart is exploited to get an analogue of the information theoretic inequality $I(X;S)\le I((X,H);S)$ in terms of diversity. It provides a lower bound on the performance of non-coherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced sub tasks. Moreover a geometrical criterion for high performance space time code design is derived. | Geometrical relations between space time block code designs and
complexity reduction | 7,040 |
We explore the available degrees of freedom for various multiuser MIMO communication scenarios such as the multiple access, broadcast, interference, relay, X and Z channels. For the two user MIMO interference channel, we find a general inner bound and a genie-aided outer bound that give us the exact number of degrees of freedom in many cases. We also study a share-and-transmit scheme for transmitter cooperation. For the share-and-transmit scheme, we show how the gains of transmitter cooperation are entirely offset by the cost of enabling that cooperation so that the available degrees of freedom are not increased. | Degrees of Freedom in Multiuser MIMO | 7,041 |
Optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission such link adaption is performed by pulse shaping which in turn is equivalent to precoding with respect to the second order channel statistics. In the present framework a translation of the precoder optimization problem into an optimization problem over trace class operators is used. This problem which is also well-known in the context of quantum information theory is unsolved in general due to its non-convex nature. However in very low dimension the problem formulation reveals an additional analytic structure which again admits the solution to the optimal precoder and multiplexing scheme. Hence, in this contribution the analytic solution of the problem for the 2x2 doubly--dispersive WSSUS channel is presented. | Precoding for 2x2 Doubly-Dispersive WSSUS Channels | 7,042 |
In this paper we consider the computation of channel capacity for ergodic multiple-input multiple-output channels with additive white Gaussian noise. Two scenarios are considered. Firstly, a time-varying channel is considered in which both the transmitter and the receiver have knowledge of the channel realization. The optimal transmission strategy is water-filling over space and time. It is shown that this may be achieved in a causal, indeed instantaneous fashion. In the second scenario, only the receiver has perfect knowledge of the channel realization, while the transmitter has knowledge of the channel gain probability law. In this case we determine an optimality condition on the input covariance for ergodic Gaussian vector channels with arbitrary channel distribution under the condition that the channel gains are independent of the transmit signal. Using this optimality condition, we find an iterative algorithm for numerical computation of optimal input covariance matrices. Applications to correlated Rayleigh and Ricean channels are given. | Optimal Transmit Covariance for Ergodic MIMO Channels | 7,043 |
For a given blocklength we determine the number of interleavers which have spread equal to two. Using this, we find out the probability that a randomly chosen interleaver has spread two. We show that as blocklength increases, this probability increases but very quickly converges to the value $1-e^{-2} \approx 0.8647$. Subsequently, we determine a lower bound on the probability of an interleaver having spread at least $s$. We show that this lower bound converges to the value $e^{-2(s-2)^{2}}$, as the blocklength increases. | On the Spread of Random Interleaver | 7,044 |
In an ultra wideband (UWB) impulse radio (IR) system, a number of pulses, each transmitted in an interval called a "frame", is employed to represent one information symbol. Conventionally, a single type of UWB pulse is used in all frames of all users. In this paper, IR systems with multiple types of UWB pulses are considered, where different types of pulses can be used in different frames by different users. Both stored-reference (SR) and transmitted-reference (TR) systems are considered. First, the spectral properties of a multi-pulse IR system with polarity randomization is investigated. It is shown that the average power spectral density is the average of the spectral contents of different pulse shapes. Then, approximate closed-form expressions for the bit error probability of a multi-pulse SR-IR system are derived for RAKE receivers in asynchronous multiuser environments. The effects of both inter-frame interference (IFI) and multiple-access interference (MAI) are analyzed. The theoretical and simulation results indicate that SR-IR systems that are more robust against IFI and MAI than a "conventional" SR-IR system can be designed with multiple types of ultra-wideband pulses. Finally, extensions to multi-pulse TR-IR systems are briefly described. | Ultra Wideband Impulse Radio Systems with Multiple Pulse Types | 7,045 |
Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However most of the proposed solutions require distributed space-time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme, that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of M available relays and then uses this best relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space-time coding for M nodes is required, such as those proposed in [7]. The simplicity of the technique, allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability and efficiency in future 4G wireless systems. | A Simple Cooperative Diversity Method Based on Network Path Selection | 7,046 |
It is shown that while the mutual information curves for coded modulation (CM) and bit interleaved coded modulation (BICM) overlap in the case of a single input single output channel, the same is not true in multiple input multiple output (MIMO) channels. A method for mitigating fading in the presence of multiple transmit antennas, named coordinate interleaving (CI), is presented as a generalization of component interleaving for a single transmit antenna. The extent of any advantages of CI over BICM, relative to CM, is analyzed from a mutual information perspective; the analysis is based on an equivalent parallel channel model for CI. Several expressions for mutual information in the presence of CI and multiple transmit and receive antennas are derived. Results show that CI gives higher mutual information compared to that of BICM if proper signal mappings are used. Effects like constellation rotation in the presence of CI are also considered and illustrated; it is shown that constellation rotation can increase the constrained capacity. | On Interleaving Techniques for MIMO Channels and Limitations of Bit
Interleaved Coded Modulation | 7,047 |
M-ary On-Off Frequency-Shift-Keying (OOFSK) is a digital modulation format in which M-ary FSK signaling is overlaid on On/Off keying. This paper investigates the potential of this modulation format in the context of wideband fading channels. First it is assumed that the receiver uses energy detection for the reception of OOFSK signals. Capacity expressions are obtained for the cases in which the receiver has perfect and imperfect fading side information. Power efficiency is investigated when the transmitter is subject to a peak-to-average power ratio (PAR) limitation or a peak power limitation. It is shown that under a PAR limitation, it is extremely power inefficient to operate in the very low SNR regime. On the other hand, if there is only a peak power limitation, it is demonstrated that power efficiency improves as one operates with smaller SNR and vanishing duty factor. Also studied are the capacity improvements that accrue when the receiver can track phase shifts in the channel or if the received signal has a specular component. To take advantage of those features, the phase of the modulation is also allowed to carry information. | On-Off Frequency-Shift-Keying for Wideband Fading Channels | 7,048 |
L multiple descriptions of a vector Gaussian source for individual and central receivers are investigated. The sum rate of the descriptions with covariance distortion measure constraints, in a positive semidefinite ordering, is exactly characterized. For two descriptions, the entire rate region is characterized. Jointly Gaussian descriptions are optimal in achieving the limiting rates. The key component of the solution is a novel information-theoretic inequality that is used to lower bound the achievable multiple description rates. | Vector Gaussian Multiple Description with Individual and Central
Receivers | 7,049 |
Mobile communication channels are often modeled as linear time-varying filters or, equivalently, as time-frequency integral operators with finite support in time and frequency. Such a characterization inherently assumes the signals are narrowband and may not be appropriate for wideband signals. In this paper time-scale characterizations are examined that are useful in wideband time-varying channels, for which a time-scale integral operator is physically justifiable. A review of these time-frequency and time-scale characterizations is presented. Both the time-frequency and time-scale integral operators have a two-dimensional discrete characterization which motivates the design of time-frequency or time-scale rake receivers. These receivers have taps for both time and frequency (or time and scale) shifts of the transmitted signal. A general theory of these characterizations which generates, as specific cases, the discrete time-frequency and time-scale models is presented here. The interpretation of these models, namely, that they can be seen to arise from processing assumptions on the transmit and receive waveforms is discussed. Out of this discussion a third model arises: a frequency-scale continuous channel model with an associated discrete frequency-scale characterization. | Canonical time-frequency, time-scale, and frequency-scale
representations of time-varying channels | 7,050 |
We determine the rate region of the quadratic Gaussian two-encoder source-coding problem. This rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression. Furthermore, this architecture requires higher rates to send a Gaussian source than it does to send any other source with the same covariance. Our techniques can also be used to determine the sum rate of some generalizations of this classical problem. Our approach involves coupling the problem to a quadratic Gaussian ``CEO problem.'' | Rate Region of the Quadratic Gaussian Two-Encoder Source-Coding Problem | 7,051 |
We identify the common underlying form of the capacity expression that is applicable to both cases where causal or non-causal side information is made available to the transmitter. Using this common form we find that for the single user channel, the multiple access channel, the degraded broadcast channel, and the degraded relay channel, the sum capacity with causal and non-causal side information are identical when all the transmitter side information is also made available to all the receivers. A genie-aided outerbound is developed that states that when a genie provides $n$ bits of side information to a receiver the resulting capacity improvement can not be more than $n$ bits. Combining these two results we are able to bound the relative capacity advantage of non-causal side information over causal side information for both single user as well as various multiple user communication scenarios. Applications of these capacity bounds are demonstrated through examples of random access channels. Interestingly, the capacity results indicate that the excessive MAC layer overheads common in present wireless systems may be avoided through coding across multiple access blocks. It is also shown that even one bit of side information at the transmitter can result in unbounded capacity improvement. As a side, we obtain the sum capacity for a multiple access channel when the side information available to the transmitter is causal and possibly correlated to the side information available to the receiver. | Capacity with Causal and Non-Causal Side Information - A Unified View | 7,052 |
We provide a counterexample to Cover's conjecture that the feedback capacity $C_\textrm{FB}$ of an additive Gaussian noise channel under power constraint $P$ be no greater than the nonfeedback capacity $C$ of the same channel under power constraint $2P$, i.e., $C_\textrm{FB}(P) \le C(2P)$. | A Counterexample to Cover's 2P Conjecture on Gaussian Feedback Capacity | 7,053 |
We consider a communication system in which the outputs of a Markov source are encoded and decoded in \emph{real-time} by a finite memory receiver, and the distortion measure does not tolerate delays. The objective is to choose designs, i.e. real-time encoding, decoding and memory update strategies that minimize a total expected distortion measure. This is a dynamic team problem with non-classical information structure [Witsenhausen:1971]. We use the structural results of [Teneketzis:2004] to develop a sequential decomposition for the finite and infinite horizon problems. Thus, we obtain a systematic methodology for the determination of jointly optimal encoding decoding and memory update strategies for real-time point-to-point communication systems. | A Decision Theoretic Framework for Real-Time Communication | 7,054 |
The potential benefits of multiple-antenna systems may be limited by two types of channel degradations rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multiple-input multiple-output (MIMO) systems, with an emphasis on orthogonal space-time block codes, in terms of the symbol error probability, the effective fading figure (EFF), and the capacity at low signal-to-noise ratio (SNR). In particular, we consider a general family of MIMO channels known as double-scattering channels, which encompasses a variety of propagation environments from independent and identically distributed Rayleigh to degenerate keyhole or pinhole cases by embracing both rank-deficient and spatial correlation effects. It is shown that a MIMO system with $n_T$ transmit and $n_R$ receive antennas achieves the diversity of order $\frac{\n_T n_S n_R}{\max(n_T,n_S,n_R)}$ in a double-scattering channel with $n_S$ effective scatterers. We also quantify the combined effect of the spatial correlation and the lack of scattering richness on the EFF and the low-SNR capacity in terms of the correlation figures of transmit, receive, and scatterer correlation matrices. We further show the monotonicity properties of these performance measures with respect to the strength of spatial correlation, characterized by the eigenvalue majorization relations of the correlation matrices. | MIMO Diversity in the Presence of Double Scattering | 7,055 |
This paper investigates the limits of information transfer over a fast Rayleigh fading MIMO channel, where neither the transmitter nor the receiver has the knowledge of the channel state information (CSI) except the fading statistics. We develop a scalar channel model due to absence of the phase information in non-coherent Rayleigh fading and derive a capacity supremum with the number of receive antennas at any signal to noise ratio (SNR) using Lagrange optimisation. Also, we conceptualise the discrete nature of the optimal input distribution by posing the optimisation on the channel mutual information for $N$ discrete inputs. Furthermore, we derive an expression for the asymptotic capacity when the input power is large, and compare with the existing capacity results when the receiver is equipped with a large number of antennas. | Non-coherent Rayleigh fading MIMO channels: Capacity Supremum | 7,056 |
We propose a computationally efficient multilevel coding scheme to achieve the capacity of an ISI channel using layers of binary inputs. The transmitter employs multilevel coding with linear mapping. The receiver uses multistage decoding where each stage performs a separate linear minimum mean square error (LMMSE) equalization and decoding. The optimality of the scheme is due to the fact that the LMMSE equalizer is information lossless in an ISI channel when signal to noise ratio is sufficiently low. The computational complexity is low and scales linearly with the length of the channel impulse response and the number of layers. The decoder at each layer sees an equivalent AWGN channel, which makes coding straightforward. | A Capacity Achieving and Low Complexity Multilevel Coding Scheme for ISI
Channels | 7,057 |
This paper introduces a new trellis pruning method which uses nonlinear convolutional coding for peak-to-average power ratio (PAPR) reduction of filtered QPSK and 16-QAM modulations. The Nyquist filter is viewed as a convolutional encoder that controls the analog waveforms of the filter output directly. Pruning some edges of the encoder trellis can effectively reduce the PAPR. The only tradeoff is a slightly lower channel capacity and increased complexity. The paper presents simulation results of the pruning action and the resulting PAPR, and also discusses the decoding algorithm and the capacity of the filtered and pruned QPSK and 16-QAM modulations on the AWGN channel. Simulation results show that the pruning method reduces the PAPR significantly without much damage to capacity. | Trellis Pruning for Peak-to-Average Power Ratio Reduction | 7,058 |
There is a fundamental relationship between belief propagation and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detail in a companion paper. This paper investigates the extension to general memoryless channels (paying special attention to the binary case). An area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed. We show that this area theorem gives rise to an upper-bound on the maximum a posteriori threshold for sparse graph codes. In situations where this bound is tight, the extrinsic soft bit estimates delivered by the belief propagation decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold. More generally, it is conjectured that the fundamental relationship between the maximum a posteriori and the belief propagation decoder which was observed for transmission over the binary erasure channel carries over to the general case. We finally demonstrate that in order for the design rate of an ensemble to approach the capacity under belief propagation decoding the component codes have to be perfectly matched, a statement which is well known for the special case of transmission over the binary erasure channel. | The Generalized Area Theorem and Some of its Consequences | 7,059 |
We present an analysis, under iterative decoding, of coset LDPC codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random-coset analysis to produce an effect that is similar to output-symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1 dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop EXIT charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the AWGN channel, including results within 0.56 dB of the unconstrained Shannon limit (i.e. not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz. | Design and Analysis of Nonbinary LDPC Codes for Arbitrary
Discrete-Memoryless Channels | 7,060 |
We consider a model for secrecy generation, with three terminals, by means of public interterminal communication, and examine the problem of characterizing all the rates at which all three terminals can generate a ``secret key,'' and -- simultaneously -- two designated terminals can generate a ``private key'' which is effectively concealed from the remaining terminal; both keys are also concealed from an eavesdropper that observes the public communication. Inner and outer bounds for the ``secret key--private key capacity region'' are derived. Under a certain special condition, these bounds coincide to yield the (exact) secret key--private key capacity region. | The Secret Key-Private Key Capacity Region for Three Terminals | 7,061 |
We are interested in how to best communicate a (usually real valued) source to a number of destinations (sinks) over a network with capacity constraints in a collective fidelity metric over all the sinks, a problem which we call joint network-source coding. Unlike the lossless network coding problem, lossy reconstruction of the source at the sinks is permitted. We make a first attempt to characterize the set of all distortions achievable by a set of sinks in a given network. While the entire region of all achievable distortions remains largely an open problem, we find a large, non-trivial subset of it using ideas in multiple description coding. The achievable region is derived over all balanced multiple-description codes and over all network flows, while the network nodes are allowed to forward and duplicate data packets. | Joint Network-Source Coding: An Achievable Region with Diversity Routing | 7,062 |
This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using R- and S-transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser CDMA system with a minimum mean-square error linear receiver. | Eigenvalue Distributions of Sums and Products of Large Random Matrices
via Incremental Matrix Expansions | 7,063 |
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and Takeshita have recently shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. In this correspondence, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. All but one of the quadratic interleavers proposed earlier by Sun and Takeshita are found to admit a quadratic inverse, although none were explicitly designed to do so. An explanation is argued for the observation that restriction to a quadratic inverse polynomial does not narrow the pool of good quadratic interleavers for turbo codes. | On Quadratic Inverses for Quadratic Permutation Polynomials over Integer
Rings | 7,064 |
We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh-fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (p.d.f.) of the output signal-to-noise ratio (SNR), as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the p.d.f. and c.d.f. of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol error rate (SER). The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte-Carlo simulations. | Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh
Environments | 7,065 |
It is believed that a particle cannot carry more than one bit of information. It is pointed out that particle or single-particle quantum state can carry more than one bit of information. It implies that minimum energy cost of transmitting a bit will be less than the accepted limit KTlog2. | A particle can carry more than one bit of information | 7,066 |
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of error-correcting codes of rate $R$ that can be list decoded in polynomial time up to a fraction $(1-R-\eps)$ of {\em worst-case} errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory. Our codes are simple to describe: they are {\em folded Reed-Solomon codes}, which are in fact {\em exactly} Reed-Solomon (RS) codes, but viewed as a code over a larger alphabet by careful bundling of codeword symbols. Given the ubiquity of RS codes, this is an appealing feature of our result, and in fact our methods directly yield better decoding algorithms for RS codes when errors occur in {\em phased bursts}. The alphabet size of these folded RS codes is polynomial in the block length. We are able to reduce this to a constant (depending on $\eps$) using ideas concerning ``list recovery'' and expander-based codes from \cite{GI-focs01,GI-ieeejl}. Concatenating the folded RS codes with suitable inner codes also gives us polynomial time constructible binary codes that can be efficiently list decoded up to the Zyablov bound, i.e., up to twice the radius achieved by the standard GMD decoding of concatenated codes. | Explicit Codes Achieving List Decoding Capacity: Error-correction with
Optimal Redundancy | 7,067 |
By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, R\'{e}nyi proposed the first formal generalization of Shannon entropy. Using this recipe of R\'{e}nyi, one can prepare only two information measures: Shannon and R\'{e}nyi entropy. Indeed, using this formalism R\'{e}nyi characterized these additive entropies in terms of axioms of quasilinear mean. As additivity is a characteristic property of Shannon entropy, pseudo-additivity of the form $x \oplus_{q} y = x + y + (1-q)x y$ is a characteristic property of nonextensive (or Tsallis) entropy. One can apply R\'{e}nyi's recipe in the nonextensive case by replacing the linear averaging in Tsallis entropy with KN-averages and thereby imposing the constraint of pseudo-additivity. In this paper we show that nonextensive entropy is unique under the R\'{e}nyi's recipe, and there by give a characterization. | Uniqueness of Nonextensive entropy under Renyi's Recipe | 7,068 |
A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver (similar to [6]) is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI--a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm of the bandwidth. Our coding scheme is motivated from the Gel'fand-Pinsker [2,3] coding and dirty paper coding [4]. Nonetheless, for our case, only causal CSI is required at the transmitter in contrast with dirty-paper coding and Gel'fand-Pinsker coding, where non-causal CSI is required. Then we consider a general discrete channel with i.i.d. states. Each input has an associated cost and a zero cost input "0" exists. The channel state is assumed be to be known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve this capacity. Later, a novel orthogonal coding scheme is proposed for the case of causal transmitter CSI and a condition for equivalence of capacity per unit cost for causal and non-causal transmitter CSI is derived. Finally, some connections are made to the case of non-causal transmitter CSI in [8]. | Writing on Fading Paper and Causal Transmitter CSI | 7,069 |
We investigate energy-efficiency issues and resource allocation policies for time division multi-access (TDMA) over fading channels in the power-limited regime. Supposing that the channels are frequency-flat block-fading and transmitters have full or quantized channel state information (CSI), we first minimize power under a weighted sum-rate constraint and show that the optimal rate and time allocation policies can be obtained by water-filling over realizations of convex envelopes of the minima for cost-reward functions. We then address a related minimization under individual rate constraints and derive the optimal allocation policies via greedy water-filling. Using water-filling across frequencies and fading states, we also extend our results to frequency-selective channels. Our approaches not only provide fundamental power limits when each user can support an infinite number of capacity-achieving codebooks, but also yield guidelines for practical designs where users can only support a finite number of adaptive modulation and coding (AMC) modes with prescribed symbol error probabilities, and also for systems where only discrete-time allocations are allowed. | Energy-Efficient Resource Allocation in Time Division Multiple-Access
over Fading Channels | 7,070 |
In the cryptanalysis of stream ciphers and pseudorandom sequences, the notions of linear, jump, and 2-adic complexity arise naturally to measure the (non)randomness of a given string. We define an isometry K on F_q^\infty that is the precise equivalent to Euclid's algorithm over the reals to calculate the continued fraction expansion of a formal power series. The continued fraction expansion allows to deduce the linear and jump complexity profiles of the input sequence. Since K is an isometry, the resulting F_q^\infty-sequence is i.i.d. for i.i.d. input. Hence the linear and jump complexity profiles may be modelled via Bernoulli experiments (for F_2: coin tossing), and we can apply the very precise bounds as collected by Revesz, among others the Law of the Iterated Logarithm. The second topic is the 2-adic span and complexity, as defined by Goresky and Klapper. We derive again an isometry, this time on the dyadic integers Z_2 which induces an isometry A on F_2}^\infty. The corresponding jump complexity behaves on average exactly like coin tossing. Index terms: Formal power series, isometry, linear complexity, jump complexity, 2-adic complexity, 2-adic span, law of the iterated logarithm, Levy classes, stream ciphers, pseudorandom sequences | Continued Fraction Expansion as Isometry: The Law of the Iterated
Logarithm for Linear, Jump, and 2--Adic Complexity | 7,071 |
A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multi-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference is large and independent across users we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed. | Carbon Copying Onto Dirty Paper | 7,072 |
The capacity region of the multiple access channel with arbitrarily correlated sources remains an open problem. Cover, El Gamal and Salehi gave an achievable region in the form of single-letter entropy and mutual information expressions, without a single-letter converse. Cover, El Gamal and Salehi also gave a converse in terms of some n-letter mutual informations, which are incomputable. In this paper, we derive an upper bound for the sum rate of this channel in a single-letter expression by using spectrum analysis. The incomputability of the sum rate of Cover, El Gamal and Salehi scheme comes from the difficulty of characterizing the possible joint distributions for the n-letter channel inputs. Here we introduce a new data processing inequality, which leads to a single-letter necessary condition for these possible joint distributions. We develop a single-letter upper bound for the sum rate by using this single-letter necessary condition on the possible joint distributions. | A Single-letter Upper Bound for the Sum Rate of Multiple Access Channels
with Correlated Sources | 7,073 |
We derive the density evolution equations for non-binary low-density parity-check (LDPC) ensembles when transmission takes place over the binary erasure channel. We introduce ensembles defined with respect to the general linear group over the binary field. For these ensembles the density evolution equations can be written compactly. The density evolution for the general linear group helps us in understanding the density evolution for codes defined with respect to finite fields. We compute thresholds for different alphabet sizes for various LDPC ensembles. Surprisingly, the threshold is not a monotonic function of the alphabet size. We state the stability condition for non-binary LDPC ensembles over any binary memoryless symmetric channel. We also give upper bounds on the MAP thresholds for various non-binary ensembles based on EXIT curves and the area theorem. | Density Evolution, Thresholds and the Stability Condition for Non-binary
LDPC Codes | 7,074 |
We prove a new outer bound on the rate-distortion region for the multiterminal source-coding problem. This bound subsumes the best outer bound in the literature and improves upon it strictly in some cases. The improved bound enables us to obtain a new, conclusive result for the binary erasure version of the "CEO problem." The bound recovers many of the converse results that have been established for special cases of the problem, including the recent one for the Gaussian version of the CEO problem. | An Infeasibility Result for the Multiterminal Source-Coding Problem | 7,075 |
An upper bound to the information capacity of a wavelength-division multi- plexed optical fiber communication system is derived in a model incorporating the nonlinear propagation effects of cross-phase modulation (XPM). This work is based on the paper by Mitra et al., finding lower bounds to the channel capacity, in which physical models for propagation are used to calculate statistical properties of the conditional probability distribution relating input and output in a single WDM channel. In this paper we present a tractable channel model incorporating the effects of cross phase modulation. Using this model we find an upper bound to the information capacity of the fiber optical communication channel at high SNR. The results provide physical insight into the manner in which nonlinearities degrade the information capacity. | Channel Model and Upper Bound on the Information Capacity of the Fiber
Optical Communication Channel Based on the Effects of XPM Induced
Nonlinearity | 7,076 |
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity}, per information bit, of encoding and decoding. It also introduces symmetry properties which play a central role in the construction of capacity-achieving ensembles for the BEC with bounded complexity. The results here improve on the tradeoff between performance and complexity provided by previous constructions of capacity-achieving ensembles of codes defined on graphs. The superiority of ARA codes with moderate to large block length is exemplified by computer simulations which compare their performance with those of previously reported capacity-achieving ensembles of LDPC and IRA codes. The ARA codes also have the advantage of being systematic. | Capacity-Achieving Ensembles of Accumulate-Repeat-Accumulate Codes for
the Erasure Channel with Bounded Complexity | 7,077 |
We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sum-rate optimal point on the boundary of the multipleaccess channel capacity region is the unique Nash Equilibrium of the corresponding water-filling game. This result sheds a new light on the opportunistic communication principle and argues for the fairness of the sum-rate optimal point, at least from a game theoretic perspective. The base-station is then introduced as a player interested in maximizing a weighted sum of the individual rates. We propose a Stackelberg formulation in which the base-station is the designated game leader. In this set-up, the base-station announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. We show that this formulation allows for achieving all the corner points of the capacity region, in addition to the sum-rate optimal point. On the negative side, we prove the non-existence of a base-station strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, we present a repeated game approach which achieves the capacity region of the fading multiple access channel. Finally, we extend our study to vector channels highlighting interesting differences between this scenario and the scalar channel case. | The Water-Filling Game in Fading Multiple Access Channels | 7,078 |
A game-theoretic model for studying power control in multi-carrier CDMA systems is proposed. Power control is modeled as a non-cooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per Joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multi-dimensional nature of users' strategies and the non-quasiconcavity of the utility function make the multi-carrier problem much more challenging than the single-carrier or throughput-based-utility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimum-mean-square-error (MMSE) detector, a user's utility is maximized when the user transmits only on its "best" carrier. This is the carrier that requires the least amount of power to achieve a particular target signal-to-interference-plus-noise ratio (SINR) at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is also characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared to a single-carrier system and also to a multi-carrier system in which each user maximizes its utility over each carrier independently. | A Game-Theoretic Approach to Energy-Efficient Power Control in
Multi-Carrier CDMA Systems | 7,079 |
Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. Our main contribution is a precise characterization of codes that are universally tradeoff-optimal, i.e., they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel. We denote this characterization as one of approximate universality where the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains, respectively. The characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space-time coding literature. | Approximately Universal Codes over Slow Fading Channels | 7,080 |
We are interested in how to best communicate a real valued source to a number of destinations (sinks) over a network with capacity constraints in a collective fidelity metric over all the sinks, a problem which we call joint network-source coding. It is demonstrated that multiple description codes along with proper diversity routing provide a powerful solution to joint network-source coding. A systematic optimization approach is proposed. It consists of optimizing the network routing given a multiple description code and designing optimal multiple description code for the corresponding optimized routes. | A Practical Approach to Joint Network-Source Coding | 7,081 |
Perfect space-time codes were first introduced by Oggier et. al. to be the space-time codes that have full rate, full diversity-gain, non-vanishing determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping of the constellation. These defining conditions jointly correspond to optimality with respect to the Zheng-Tse D-MG tradeoff, independent of channel statistics, as well as to near optimality in maximizing mutual information. All the above traits endow the code with error performance that is currently unmatched. Yet perfect space-time codes have been constructed only for 2,3,4 and 6 transmit antennas. We construct minimum and non-minimum delay perfect codes for all channel dimensions. | Perfect Space-Time Codes with Minimum and Non-Minimum Delay for Any
Number of Antennas | 7,082 |
This paper consists of two parts. In the first part, we develop a new information theory, in which it is not a coincidence that information and physical entropy share the same mathematical formula. It is an adaptation of mind to help search for resources. We then show that psychological patterns either reflect the constraints of physical laws or are evolutionary adaptations to efficiently process information and to increase the chance of survival in the environment of our evolutionary past. In the second part, we demonstrate that the new information theory provides the foundation to understand market behavior. One fundamental result from the information theory is that information is costly. In general, information with higher value is more costly. Another fundamental result from the information theory is that the amount of information one can receive is the amount of information generated minus equivocation. The level of equivocation, which is the measure of information asymmetry, is determined by the correlation between the source of information and the receiver of information. In general, how much information one can receive depends on the background knowledge of the receiver. The difference in cost different investors are willing to pay for information and the difference in background knowledge about a particular information causes the heterogeneity in information processing by the investment public, which is the main reason of the price and volume patterns observed in the market. Many assumptions in some of the recent models on behavioral finance can be derived naturally from this theory. | The Physical Foundation of Human Mind and a New Theory of Investment | 7,083 |
In this work we explicitly provide the first ever optimal, with respect to the Zheng-Tse diversity multiplexing gain (D-MG) tradeoff, cooperative diversity schemes for wireless relay networks. The schemes are based on variants of perfect space-time codes and are optimal for any number of users and all statistically symmetric (and in some cases, asymmetric) fading distributions. We deduce that, with respect to the D-MG tradeoff, channel knowledge at the intermediate relays and infinite delay are unnecessary. We also show that the non-dynamic selection decode and forward strategy, the non-dynamic amplify and forward, the non-dynamic receive and forward, the dynamic amplify and forward and the dynamic receive and forward cooperative diversity strategies allow for exactly the same D-MG optimal performance. | Approximately universal optimality over several dynamic and non-dynamic
cooperative diversity schemes for wireless networks | 7,084 |
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as the length of the code goes to infinity via recent results in random hypergraphs [Darling-Norris 2005]. For a code of finite length, we provide an algorithm for computing the probability of error of the decoder. This algorithm improves the one of [Karp-Luby-Shokrollahi 2004] by a linear factor. | New model for rigorous analysis of LT-codes | 7,085 |
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem is shown as a similar special case. A spatial concentration of radio signals example is provided, and it is shown that an uncertainty principle exists for concentration of single-frequency signals for regions in space. We show that the uncertainty is related to the volumes of the spatial regions. | Uncertainty Principles for Signal Concentrations | 7,086 |
In this paper, we introduce the novel use of linear spatial precoding based on fixed and known parameters of multiple-input multiple-output (MIMO) channels to improve the performance of space-time coded MIMO systems. We derive linear spatial precoding schemes for both coherent (channel is known at the receiver) and non-coherent (channel is un-known at the receiver) space-time coded MIMO systems. Antenna spacing and antenna placement (geometry) are considered as fixed parameters of MIMO channels, which are readily known at the transmitter. These precoding schemes exploit the antenna placement information at both ends of the MIMO channel to ameliorate the effect of non-ideal antenna placement on the performance of space-time coded systems. In these schemes, the precoder is fixed for given transmit and receive antenna configurations and transmitter does not require any feedback of channel state information (partial or full) from the receiver. Closed form solutions for both precoding schemes are presented for systems with up to three receiver antennas. A generalized method is proposed for more than three receiver antennas. We use the coherent space-time block codes (STBC) and differential space-time block codes to analyze the performance of proposed precoding schemes. Simulation results show that at low SNRs, both precoders give significant performance improvement over a non-precoded system for small antenna aperture sizes. | Spatial Precoder Design for Space-Time Coded MIMO Systems: Based on
Fixed Parameters of MIMO Channels | 7,087 |
We estimate the variance of weight and stopping set distribution of regular LDPC ensembles. Using this estimate and the second moment method we obtain bounds on the probability that a randomly chosen code from regular LDPC ensemble has its weight distribution and stopping set distribution close to respective ensemble averages. We are able to show that a large fraction of total number of codes have their weight and stopping set distribution close to the average. | On the Asymptotic Weight and Stopping Set Distribution of Regular LDPC
Ensembles | 7,088 |
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen's based bounds and their improvements, sphere-packing bounds, and information-theoretic bounds on the bit error probability of codes defined on graphs. A comprehensive overview is provided in a monograph by the authors which is currently in preparation. | Analytical Bounds on Maximum-Likelihood Decoded Linear Codes with
Applications to Turbo-Like Codes: An Overview | 7,089 |
The paper is focused on the tradeoff between performance and decoding complexity per iteration for LDPC codes in terms of their gap (in rate) to capacity. The study of this tradeoff is done via information-theoretic bounds which also enable to get an indication on the sub-optimality of message-passing iterative decoding algorithms (as compared to optimal ML decoding). The bounds are generalized for parallel channels, and are applied to ensembles of punctured LDPC codes where both intentional and random puncturing are addressed. This work suggests an improvement in the tightness of some information-theoretic bounds which were previously derived by Burshtein et al. and by Sason and Urbanke. | Performance versus Complexity Per Iteration for Low-Density Parity-Check
Codes: An Information-Theoretic Approach | 7,090 |
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where these channels are memoryless, binary-input and output-symmetric (MBIOS). The bounds are applied to punctured LDPC codes. A diagram concludes our discussion by showing interconnections between the theorems in this paper and some previously reported results. | On Achievable Rates and Complexity of LDPC Codes for Parallel Channels:
Information-Theoretic Bounds and Applications | 7,091 |
The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes. To this end we introduce the concept of graph-cover decoding. Whereas in maximum-likelihood decoding all codewords in a code are competing to be the best explanation of the received vector, under graph-cover decoding all codewords in all finite covers of a Tanner graph representation of the code are competing to be the best explanation. We are interested in graph-cover decoding because it is a theoretical tool that can be used to show connections between linear programming decoding and message-passing iterative decoding. Namely, on the one hand it turns out that graph-cover decoding is essentially equivalent to linear programming decoding. On the other hand, because iterative, locally operating decoding algorithms like message-passing iterative decoding cannot distinguish the underlying Tanner graph from any covering graph, graph-cover decoding can serve as a model to explain the behavior of message-passing iterative decoding. Understanding the behavior of graph-cover decoding is tantamount to understanding the so-called fundamental polytope. Therefore, we give some characterizations of this polytope and explain its relation to earlier concepts that were introduced to understand the behavior of message-passing iterative decoding for finite-length codes. | Graph-Cover Decoding and Finite-Length Analysis of Message-Passing
Iterative Decoding of LDPC Codes | 7,092 |
We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood models. We provide invariant estimators of the model parameters and formulate conditions under which these estimators are essentially posteriori unbiased for gaussian models. An upper bound on the coarseness of discretization on the model parameters is deduced. We introduce a discrimination measure between probability distributions and use it to construct probability distributions on model classes. The total code length is shown to equal the NML code length of Rissanen to within an additive constant when choosing Jeffreys prior distribution on the model parameters together with a particular choice of prior distribution on the model classes. Our model selection principle is applied to a gaussian estimation problem for data in a wavelet representation and its performance is tested and compared to alternative wavelet-based estimation methods in numerical experiments | An invariant bayesian model selection principle for gaussian data in a
sparse representation | 7,093 |
In this letter we present a new construction of interleavers for turbo codes from 3-regular Hamiltonian graphs. The interleavers can be generated using a few parameters, which can be selected in such a way that the girth of the interleaver graph (IG) becomes large, inducing a high summary distance. The size of the search space for these parameters is derived. The proposed interleavers themselves work as their de-interleavers. | Construction of Turbo Code Interleavers from 3-Regular Hamiltonian
Graphs | 7,094 |
Gaussian channels with memory and with noiseless feedback have been widely studied in the information theory literature. However, a coding scheme to achieve the feedback capacity is not available. In this paper, a coding scheme is proposed to achieve the feedback capacity for Gaussian channels. The coding scheme essentially implements the celebrated Kalman filter algorithm, and is equivalent to an estimation system over the same channel without feedback. It reveals that the achievable information rate of the feedback communication system can be alternatively given by the decay rate of the Cramer-Rao bound of the associated estimation system. Thus, combined with the control theoretic characterizations of feedback communication (proposed by Elia), this implies that the fundamental limitations in feedback communication, estimation, and control coincide. This leads to a unifying perspective that integrates information, estimation, and control. We also establish the optimality of the Kalman filtering in the sense of information transmission, a supplement to the optimality of Kalman filtering in the sense of information processing proposed by Mitter and Newton. In addition, the proposed coding scheme generalizes the Schalkwijk-Kailath codes and reduces the coding complexity and coding delay. The construction of the coding scheme amounts to solving a finite-dimensional optimization problem. A simplification to the optimal stationary input distribution developed by Yang, Kavcic, and Tatikonda is also obtained. The results are verified in a numerical example. | Gaussian Channels with Feedback: Optimality, Fundamental Limitations,
and Connections of Communication, Estimation, and Control | 7,095 |
We investigate the computation of Csiszar's bounds for the joint source-channel coding (JSCC) error exponent, E_J, of a communication system consisting of a discrete memoryless source and a discrete memoryless channel. We provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained. These equivalent representations can be readily computed for arbitrary source-channel pairs via Arimoto's algorithm. When the channel's distribution satisfies a symmetry property, the bounds admit closed-form parametric expressions. We then use our results to provide a systematic comparison between the JSCC error exponent E_J and the tandem coding error exponent E_T, which applies if the source and channel are separately coded. It is shown that E_T <= E_J <= 2E_T. We establish conditions for which E_J > E_T and for which E_J = 2E_T. Numerical examples indicate that E_J is close to 2E_T for many source-channel pairs. This gain translates into a power saving larger than 2 dB for a binary source transmitted over additive white Gaussian noise channels and Rayleigh fading channels with finite output quantization. Finally, we study the computation of the lossy JSCC error exponent under the Hamming distortion measure. | On the Joint Source-Channel Coding Error Exponent for Discrete
Memoryless Systems: Computation and Comparison with Separate Coding | 7,096 |
We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called ``anytime capacity'' is shown to be necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback. In cases of sufficiently rich information patterns between the encoder and decoder, adequate anytime capacity is also shown to be sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations, delayed control actions, and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to continuous time systems as well. We close with comments discussing a hierarchy of difficulty for communication problems and how these results establish where stabilization problems sit in that hierarchy. | The necessity and sufficiency of anytime capacity for stabilization of a
linear system over a noisy communication link Part I: scalar systems | 7,097 |
The capacity of peak-power limited, single-antenna, non-coherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. | Gaussian Fading is the Worst Fading | 7,098 |
We provide a tight approximate characterization of the $n$-dimensional product multicommodity flow (PMF) region for a wireless network of $n$ nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in both an information theoretic sense and for a combinatorial interference model (e.g., Protocol model). These provide an inner approximation to the $n^2$ dimensional capacity region. These results answer the following questions which arise naturally from previous work: (a) What is the significance of $1/\sqrt{n}$ in the scaling laws for the Protocol interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a tight approximation to the "maximum supportable flow" for node distributions more general than the geometric random distribution, traffic models other than randomly chosen source-destination pairs, and under very general assumptions on the channel fading model? We first establish that the random source-destination model is essentially a one-dimensional approximation to the capacity region, and a special case of product multi-commodity flow. Building on previous results, for a combinatorial interference model given by a network and a conflict graph, we relate the product multicommodity flow to the spectral properties of the underlying graphs resulting in computational upper and lower bounds. For the more interesting random fading model with additive white Gaussian noise (AWGN), we show that the scaling laws for PMF can again be tightly characterized by the spectral properties of appropriately defined graphs. As an implication, we obtain computationally efficient upper and lower bounds on the PMF for any wireless network with a guaranteed approximation factor. | Product Multicommodity Flow in Wireless Networks | 7,099 |
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