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The CRC used in the Modem Protocol is an alternate form of block check
which provides more robust error detection than the original checksum.
Andrew S. Tanenbaum says in his book, Computer Networks, that the CRC-
CCITT used by the Modem Protocol will detect all single and double bit
errors, all errors with an odd number of bits, all burst errors of length
16 or less, 99.997% of 17-bit error bursts, and 99.998% of 18-bit and
longer bursts.[1]
The changes to the Modem Protocol to replace the checksum with the CRC are
straight forward. If that were all that we did we would not be able to
communicate between a program using the old checksum protocol and one
using the new CRC protocol. An initial handshake was added to solve this
problem. The handshake allows a receiving program with CRC capability to
determine whether the sending program supports the CRC option, and to
switch it to CRC mode if it does. This handshake is designed so that it
will work properly with programs which implement only the original
protocol. A description of this handshake is presented in section 10.
Figure 10. Message Block Level Protocol, CRC mode
Each block of the transfer in CRC mode looks like:
<SOH><blk #><255-blk #><--128 data bytes--><CRC hi><CRC lo>
in which:
<SOH> = 01 hex
<blk #> = binary number, starts at 01 increments by 1, and
wraps 0FFH to 00H (not to 01)
<255-blk #> = ones complement of blk #.
<CRC hi> = byte containing the 8 hi order coefficients of the CRC.
<CRC lo> = byte containing the 8 lo order coefficients of the CRC.
8.1 CRC Calculation
8.1.1 Formal_Definition
To calculate the 16 bit CRC the message bits are considered to be the
coefficients of a polynomial. This message polynomial is first multiplied
by X^16 and then divided by the generator polynomial (X^16 + X^12 + X^5 +
__________
1. This reliability figure is misleading because XMODEM's critical
supervisory functions are not protected by this CRC.
Chapter 8 Xmodem Protocol Overview
X/YMODEM Protocol Reference 10-27-87 23
1) using modulo two arithmetic. The remainder left after the division is
the desired CRC. Since a message block in the Modem Protocol is 128 bytes
or 1024 bits, the message polynomial will be of order X^1023. The hi order
bit of the first byte of the message block is the coefficient of X^1023 in
the message polynomial. The lo order bit of the last byte of the message
block is the coefficient of X^0 in the message polynomial.
Figure 11. Example of CRC Calculation written in C
The following XMODEM crc routine is taken from "rbsb.c". Please refer to
the source code for these programs (contained in RZSZ.ZOO) for usage. A
fast table driven version is also included in this file.
/* update CRC */
unsigned short
updcrc(c, crc)
register c;
register unsigned crc;
{
register count;
for (count=8; --count>=0;) {
if (crc & 0x8000) {
crc <<= 1;
crc += (((c<<=1) & 0400) != 0);
crc ^= 0x1021;
}
else {
crc <<= 1;
crc += (((c<<=1) & 0400) != 0);
}
}
return crc;
}
8.2 CRC File Level Protocol Changes
8.2.1 Common_to_Both_Sender_and_Receiver
The only change to the File Level Protocol for the CRC option is the
initial handshake which is used to determine if both the sending and the
receiving programs support the CRC mode. All Modem Programs should support