Channel Codes

BCH and Hamming Codes

BCH codes for blocklength of up to 1023 and different error correction capability t can be downloaded. Note, that Hamming codes are BCH codes with t=1. BCH and Hamming codes are cyclic codes, that can be described by a parity check matrix, where each row is a shifted version of the neighboring rows (We have called this form "strip format", because the '1's form diagonal stips in the matrix).

N K Rate t Parity Check Matrix
7 4 0.57 1 matrix or alist
15 11 0.73 1 matrix or alist
15 7 0.47 2 matrix or alist
31 26 0.84 1 matrix or alist
31 21 0.68 2 matrix or alist
31 16 0.52 3 matrix or alist
31 11 0.35 5 matrix or alist
63 57 0.90 1 matrix or alist
63 51 0.81 2 matrix or alist or 1-min
63 45 0.71 3 matrix or alist or 1-min
63 39 0.62 4 matrix or alist or 1-min
63 36 0.57 5 matrix or alist or 1-min
63 30 0.48 6 matrix or alist or 1-min
127 120 0.94 1 matrix or alist
127 113 0.89 2 matrix or alist
127 106 0.83 3 matrix or alist
127 99 0.78 4 matrix or alist or 1-min
127 92 0.72 5 matrix or alist or 1-min
127 85 0.67 6 matrix or alist or 1-min
127 78 0.61 7 matrix or alist or 1-min
127 71 0.56 9 matrix or alist or 1-min
127 64 0.50 10 matrix or alist or 1-min
255 247 0.97 1 matrix or alist
255 239 0.94 2 matrix or alist or 1-min
255 231 0.91 3 matrix or alist
255 223 0.87 4 matrix or alist
255 215 0.84 5 matrix or alist
255 207 0.81 6 matrix or alist or 1-min
255 199 0.78 7 matrix or alist
255 191 0.75 8 matrix or alist
255 163 0.64 12 matrix or alist or 1-min
511 502 0.98 1 matrix or alist
511 493 0.96 2 matrix or alist
511 484 0.95 3 matrix or alist
511 475 0.93 4 matrix or alist
511 466 0.91 5 matrix or alist
511 457 0.89 6 matrix or alist
1023 1013 0.99 1 matrix or alist
1023 1003 0.98 2 matrix or alist
1023 993 0.97 3 matrix or alist
1023 983 0.96 4 matrix or alist


DVB S-2 BCH Codes

DVB S-2 uses BCH codes as an outer code (in addition to the inner LDPC). Matrices for the short frame are provided.

NKRatetParity Check Matrix
324030720.9512matrix or alist
540052320.9712matrix or alist
648063120.9712matrix or alist
720070320.9812matrix or alist
16383162150.9912matrix or alist


Extended BCH Codes

Extended BCH codes have an additional parity bit, that checks all bit positions.

NKRateParity Check Matrix
128640.5matrix or alist


Zum Seitenanfang