File size: 5,145 Bytes
8b64896 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 |
---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- error-correction
- hamming-code
---
# threshold-hamming74decoder
Hamming(7,4) decoder with single-error correction. Takes a 7-bit codeword (possibly corrupted) and outputs the corrected 4 data bits.
## Circuit Overview
```
c1 c2 c3 c4 c5 c6 c7
│ │ │ │ │ │ │
└──┴──┴──┴──┴──┴──┴─────────────────────┐
│ │ │ │ │ │ │ │
▼ ▼ ▼ ▼ ▼ ▼ ▼ │
┌─────────────────────┐ │
│ Syndrome Computer │ │
│ s1 = c1⊕c3⊕c5⊕c7 │ │
│ s2 = c2⊕c3⊕c6⊕c7 │ │
│ s3 = c4⊕c5⊕c6⊕c7 │ │
└─────────────────────┘ │
│ s1,s2,s3 │
▼ │
┌─────────────────────┐ │
│ Error Locator │ │
│ flip3 = s1∧s2∧¬s3 │ ┌──────────────┘
│ flip5 = s1∧¬s2∧s3 │ │ c3,c5,c6,c7
│ flip6 = ¬s1∧s2∧s3 │ │
│ flip7 = s1∧s2∧s3 │ │
└─────────────────────┘ │
│ │
▼ ▼
┌─────────────────────────────┐
│ Corrector │
│ d1 = c3 ⊕ flip3 │
│ d2 = c5 ⊕ flip5 │
│ d3 = c6 ⊕ flip6 │
│ d4 = c7 ⊕ flip7 │
└─────────────────────────────┘
│
▼
d1 d2 d3 d4
```
## Decoding Algorithm
**Step 1: Compute Syndrome**
The syndrome is a 3-bit value that indicates the error position:
| s3 | s2 | s1 | Decimal | Meaning |
|----|----|----|---------|---------|
| 0 | 0 | 0 | 0 | No error |
| 0 | 0 | 1 | 1 | Error in c1 (parity) |
| 0 | 1 | 0 | 2 | Error in c2 (parity) |
| 0 | 1 | 1 | 3 | Error in c3 (d1) |
| 1 | 0 | 0 | 4 | Error in c4 (parity) |
| 1 | 0 | 1 | 5 | Error in c5 (d2) |
| 1 | 1 | 0 | 6 | Error in c6 (d3) |
| 1 | 1 | 1 | 7 | Error in c7 (d4) |
**Step 2: Locate and Correct**
Only data positions (3, 5, 6, 7) need correction in the output. Parity bit errors (positions 1, 2, 4) don't affect data extraction.
**Step 3: Extract Data**
Data bits are at positions 3, 5, 6, 7 of the codeword, XORed with their flip signals.
## 4-Way XOR Implementation
Each syndrome bit requires a 4-input XOR:
```
XOR(a,b,c,d) = XOR(XOR(a,b), XOR(c,d))
a b c d
│ │ │ │
└─┬─┘ └─┬─┘
▼ ▼
┌─────┐ ┌─────┐
│ XOR │ │ XOR │ Layer 1-2
└─────┘ └─────┘
│ │
└─────┬─────┘
▼
┌─────┐
│ XOR │ Layer 3-4
└─────┘
│
▼
XOR(a,b,c,d)
```
## Architecture
| Stage | Component | Neurons | Layers |
|-------|-----------|---------|--------|
| Syndrome | 3 × 4-way XOR | 18 | 4 |
| Error Locator | 4 detectors | 4 | 1 |
| Corrector | 4 × 2-way XOR | 12 | 2 |
| **Total** | | **34** | **6** |
Note: Syndrome computation and final XOR stages run in parallel where possible.
## Error Correction Examples
```
Original: 1011 → encode → 0110011
Corrupted: 0110011 → flip bit 5 → 0110111
Syndrome: s1=1, s2=0, s3=1 → position 5
Corrected: d1=1, d2=0, d3=1, d4=1 ✓
Original: 0000 → encode → 0000000
Corrupted: 0000000 → flip bit 7 → 0000001
Syndrome: s1=1, s2=1, s3=1 → position 7
Corrected: d1=0, d2=0, d3=0, d4=0 ✓
```
## Limitations
- Corrects **single-bit** errors only
- **Detects** double-bit errors (non-zero syndrome, wrong correction)
- Cannot distinguish 2-bit errors from 1-bit errors
For stronger protection, use Hamming(7,4) + overall parity (SECDED).
## Usage
```python
from safetensors.torch import load_file
w = load_file('model.safetensors')
def hamming74_decode(codeword):
"""Decode 7-bit Hamming codeword to 4 data bits with error correction"""
# See model.py for full implementation
pass
# Received corrupted codeword (error at position 3)
received = [0, 1, 0, 0, 0, 1, 1] # Should be [0,1,1,0,0,1,1]
data = hamming74_decode(received)
# Returns [1, 0, 1, 1] (corrected)
```
## Files
```
threshold-hamming74decoder/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|