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The art of error correcting coding - Moreloz R.H.

Moreloz R.H. The art of error correcting coding - Wiley publishing , 2002. - 232 p.
ISBN 0471-49581-6
Download (direct link): artoferrorcorrecting2002.pdf
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Natural labeling, 174 Non-primitive BCH codes, 38 Non-systematic cyclic code, 35
220
THE ART OF ERROR CORRECTING CODING
Nyquist bandwidth, 169
Order of an element in GF(2m), 43 Ordered statistics decoding, 131 Orthogonal checks, 30 Outer code, 110
Parallel concatenated code, 147 Parallel decoding of multilevel codes, 185 Parity-check matrix, 6 ofBCH code, 45 of cyclic code, 36 Parity node, 159 Parity sub-matrix, 7 Partition level, 117-118 Path memory, 87, 88 Pearl’s algorithm, 162 Perfect code definition, 11 Permutation, 111 Permutation matrix, 147 PGZ algorithm, 47, 52-53 Polynomial
associated with vector, 33 erasure locator, 67 errata locator, 68 error, 46
error evaluator, 62 error locator, 47 generator, 34 minimal, 43 modified syndrome, 67 parity-check, 36 primitive, 41 syndrome, 39 Polynomial code, 27, 45 Primitive element, 41 polynomial, 41 Probability
a-posteriori, 135 AWGN, Q-function, 2 bit error, 16
bit error, BPSK over AWGN, 2 correct decoding, 14 incorrect decoding, 14 undetected error, 13 Product code, 109 decoding, 115 Projective geometry (PG) code, 45 Punctured code, 103 Punctured convolutional codes, 94 Puncturing
as shortening the dual code, 103
Q-function, 2 RCPC codes, 98
Reed-Muller (RM) code, 27, 45, 119 decoder for cyclic code, 32 majority-logic decoding, 31 number of minimum weight codewords, 29 Reed-Solomon (RS) code, 2 as polynomial code, 61 binary image of, 62
encoding as a polynomial evaluation, 61 generator polynomial, 62 weight distribution, 71 Reliability AWGN channel, 129 Repeat-and-accumulate code, 154 Repetition code example, 4, 5, 11 probability decoding error, 14 RS decoder
bound bit error probability, 72 bound word error probability, 72 error evaluator polynomial, 62 errors-and-erasures, 67 direct solution, 71 errata evaluator, 68 errata locator, 68 modified discrepancy, 68 modified Forney algorithm, 68 modified Forney syndrome, 67 Forney algorithm, 62 Massey algorithm, 63
Self-dual code, 103 Set partitioning, 174 block for unequal error protection, 185 hybrid, 183 Shannon limit, 73 Shortened code, 101 additional correctable error patterns, 102 Shortening depth, 38 Signal point, 170
Sliding window SOVA algorithm, 136 Soft decision decoding, 15 Soft-output Chase algorithm, 156 Soft-output ordered statistics algorithm, 140 SOVA algorithm, 134 Spectral efficiency, 169 Squaring construction, 108 Standard array
as look-up table, 10 construction, 9 decoding, 8 State diagram convolutional code, 74
INDEX
221
for computing weight distribution, 81 for computing weight enumerating sequence, 82, 176 Subcode property, 119 Sudan algorithm, 134 Sum-product algorithm, 162 Supercode, 104 Syndrome
as evaluation of zeros of code, 47 as vector, 9
circuit for computing, 48 Syndrome polynomial, 39 Syndrome trellis, 128 Systematic cyclic code, 35 Systematic encoding, 3
Tail-biting code, 80 Tanner graph, 159 Time-sharing code, 106 Trellis diagram, 76 Trellis structure
example 3-level coded 8-PSK modulation, 181 of array codes, 113 of block and convolutional codes, 3 Ungerboeck mapping, 174 Turbo code, 106, 143, 147
as a punctured product code, 148
component RSC code, 144 Two-dimensional code, 110 Two-stage decoding, 115, 176 Two-step majority-logic decoding, 31
Unequal error protection
multilevel modulation code, 183 Unequal error protection code, 99, 109, 118 example, 10
Vandermonde matrix, 45 Variable node, 159 Viterbi algorithm, 86-94 ACS, 94
branch synchronization, 89 traceback, 92 traceback memory, 76 Viterbi decoder off-the-shelf, 177
Weight distribution
convolutional codes, 81-84 defined, 12
extended BCH codes, 57 Weight enumerating sequence, 82
Zero-tail code, 79
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