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Morelos-Zaragoza R.H. — The art of error-correcting coding
Morelos-Zaragoza R.H. — The art of error-correcting coding



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Название: The art of error-correcting coding

Автор: Morelos-Zaragoza R.H.

Аннотация:

The Art of Error Correcting Coding provides a comprehensive coverage of the basic techniques of error concealment. It addresses the need for selecting, implementing and simulating algorithms for the encoding and decoding of codes used for error correction and detection. This practical approach uses simple and easy to follow numerical examples to describe the basic concepts of a particular coding or decoding scheme. Basic analysis tools are provided throughout to help in the assessment of the error performance block and convolutional codes of a particular Error Correcting Coding (ECC) scheme for a selection of the basic channel models.
* Provides a complete treatment of important decoding algorithms including errors-and-erasures decoding of BCH and Reed-Solomon codes for any set of consecutive zeros and any length
* Describes Viterbi decoding and the key implementation issues
* Includes soft-output decoding algorithms, MAP, log-MAP, Max-log-MAP, belief propagation and ordered statistics
* Discusses new reliability-based algorithms such as GMD and the Chase algorithm with soft outputs
* Examines turbo codes, both serially and parallel concatenated, as well as low-density parity-check (LDPC) codes and their iterative decoders
* Features a companion website providing computer programs written in C language, to help understanding and implementing basic ECC techniques
This volume provides an indispensable tool for understanding and applying ECC techniques in transmission and storage of digital information. Engineers, computer scientists and graduate students alike, will all benefit from such a practical introductory approach.


Язык: en

Рубрика: Computer science/Теория информации/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 221

Добавлена в каталог: 20.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$2^s$-ary weight of an integer      46
A-posteriori probability (APP)      122 135
Algebraic geometry codes      61
ARQ      99
Array code      113
Asymptotic coding gain      173 187
Asymptotic coding gain, greater than, with block partitioning      187
Augmented code      104
Automatic repeat request      99
AWGN channel      15 122
AWGN channel, metric, equivalence to changing sign      122
AWGN channel, reliability      129
BCH bound      45
BCH code      44
BCH code, extended      57
BCH code, general decoder      48
BCH code, how to compute weight distribution      57
BCH code, performance AWGN channel      57
BCH code, specified by zeros      45
BCH decoder, Berlekamp — Massey algorithm      47
BCH decoder, Euclidean algorithm      47
BCH decoder, general      48
BCH decoder, Massey algorithm      63
BCH decoder, PGZ algorithm      47
BCJR algorithm      137
BEC channel      55
Belief propagation decoding      162
Berlekamp — Massey algorithm      47 49—52
Berlekamp — Massey algorithm, discrepancy      49
Berlekamp — Massey algorithm, errors-and-erasures, errata evaluator      68
Berlekamp — Massey algorithm, errors-and-erasures, errata locator      68
Berlekamp — Massey algorithm, errors-and-erasures, modified discrepancy      68
Berlekamp — Massey algorithm, errors-and-erasures, modified Forney algorithm      68
Berlekamp — Massey algorithm, errors-and-erasures, modified Forney syndrome      67
Bit error probability, AWGN      2
Block code concept      3
Boolean function      27
Bound, BCH      45
Bound, bit error probability, AWGN channel      57
Bound, Chernoff      19
Bound, Hamming      11
Bound, Hamming, nonbinary case      12
Bound, RS decoder      72
Bound, union, AWGN channel      16
Bound, union, convolutional code      84
Bound, union, multilevel modulation code for UEP      186
Burst error correcting capability      113
Chase algorithm      129
Chase algorithm, soft output      156
Chase algorithm, soft output, correction factor      157
Chase algorithm, soft output, scaling factor      157
Chien search      55
Code, self-dual      7 29
Coded modulation, bit-interleaved (BICM)      189
Coded modulation, main idea      2
Coded modulation, MCM      2 173 180
Coded modulation, MCM, multistage decoding      182
Coded modulation, MCM, parallel decoding      185
Coded modulation, MCM, unequal error protection      183
Coded modulation, Pragmatic TCM, symbol transformation      177
Coded modulation, Pragmatic TCM, two-stage decoding      176
Coded modulation, TCM      2 173 174
Coded modulation, TCM, example modified state diagram      176
Coded modulation, TCM, MLD decoding      175
Coded modulation, turbo trellis(TTCM)      192
Coding gain      2 16
Coding gain, asymptotic      173 187
Complementary error function (erfc)      2
Concatenated code      115
Concatenated coding      2
Conjugate elements      43
Constellation      170
Construction X3      109
Convolutional code      2
Convolutional code, block code obtained from      79
Convolutional code, complete weight enumerator sequence      83
Convolutional code, constraint length      74
Convolutional code, defined      3
Convolutional code, direct-truncation      80
Convolutional code, finite-state machine      73
Convolutional code, generator sequences      75
Convolutional code, polynomial generator matrix      77
Convolutional code, recursive systematic (RSC code)      78
Convolutional code, RSC code      144
Convolutional code, state diagram      74
Convolutional code, tail-biting      80
Convolutional code, union bound over BSC and AWGN channels      84
Convolutional code, weight distribution block codes from      81—84
Convolutional code, weight enumerating sequence      82
Convolutional code, zero-tail code      79
Correlation discrepancy      133
Coset      104
Coset, decomposition      104 109 118
Coset, leader      10
Coset, representative      118 140
CRC code      37
CRC code, popular polynomials      38
Cycle set      43
Cyclic code, defined      33
Cyclic code, encoding by division by g(x)      36
Cyclic code, extended      57
Cyclic code, general decoder      39
Cyclic code, MLS code      37
Cyclic code, RM code      29
Cyclic code, shortened      37
Cyclic code, syndrome decoding, error-trapping      39
Cyclic code, zeros of      34
Cyclic shift      33
Cyclotomic coset      43
Decoding, BCH codes general      48
Decoding, BCJR algorithm      137
Decoding, belief propagation      162
Decoding, Berlekamp — Massey algorithm      47 49—52
Decoding, Chase algorithm      129
Decoding, Chase algorithm, soft output      156
Decoding, Chien search      55
Decoding, Depth      88
Decoding, Euclidean algorithm      47 53—54
Decoding, Forney algorithm for RS codes      62
Decoding, GMD algorithm      132
Decoding, Log-MAP algorithm      139
Decoding, look-up table      10
Decoding, MAP algorithm      137
Decoding, Massey algorithm      63
Decoding, Max-Log-MAP algorithm      140
Decoding, MLD      86 175
Decoding, Modified Forney algorithm      68
Decoding, ordered statistics algorithm      131
Decoding, ordered statistics algorithm, soft-output      140
Decoding, Parallel for multilevel codes      185
Decoding, PGZ algorithm      47 52—53
Decoding, SOVA algorithm      134
Decoding, Sudan algorithm      67 134
Decoding, SW-SOVA algorithm      136
Decoding, two-stage      115 176
Decoding, Viterbi algorithm      85—94
Decoding, with standard array      8
Decomposable code      107 117
Direct-truncation code      80
Discrepancy Berlelamp — Massey algorithm      49
Disjunctive normal form      27
Distance, designed of BCH code      44
Distance, free      79
Distance, Hamming      4
Distance, minimum Hamming      4
Distance, minimum squared Euclidean      173
Distance, squared Euclidean      15
Dual code      6
Dual code of cyclic code      37
Dual code of RM code      28
Dual code, example      7
Encoding, non-systematic      35
Encoding, recursive with parity-check matrix      36
Encoding, systematic      16 35
Encoding, with generator matrix      8
Encoding, with parity-check matrix      8
erasure      55
Erasure correction for binary linear codes      55
Erasure locator polynomial      67
Erasure, value      67
Error bursts      2
Error correcting capability      5
Error correcting code, as subset      4
Error correcting code, defined      3
Error correcting code, minimum Hamming distance      4
Error evaluator polynomial      62
Error locator polynomial      47
Error polynomial      46
Error propagation      186
Error, positions      47
Error, values      47
Euclidean algorithm      47 53—54
Euclidean algorithm, polynomials same up to a constant      66
Euclidean geometry (EG) code      45
Extended code      103
Factoring polynomials in $GF(2^m)$ is hard      55
Field      40
Field, Galois      40
Field, Galois, arithmetic      41
Field, Galois, element order      43
Field, Galois, representations      41
Finding factors of $x^{2^m-1}+1$      43
Finite geometry      28
Flat Rayleigh fading channel, bound      18
Flat Rayleigh fading channel, model      17
Forney algorithm      62
Fourier transform, BCH decoding with      67
Free distance      79
Gallager code      160
Galois field      40
Generalized concatenated code      117
Generalized concatenated code, array codes      113
Generator matrix      6
Generator polynomial      34
Generator polynomial of BCH code      44
Generator polynomial of RS code      62
GMD decoding      132
Golay code      25
greatest common divisor (GCD)      53
Hamming code      23
Hamming code, shortened (71,64.3) code      37
Hamming space, defined      4
Hamming space, distance      4
Hamming space, sphere      5
Hard-decision decoding      16
Hard-decision decoding, general structure      20
Incidence vector      29
Inner code      110
Interleaves      152
Interleaves, block      111
Interleaves, convolutional      116
Interleaves, cyclic      114
Interleaves, Ramsey      111 116 152
Interleaves, random      152
Interleaves, S—random      152
Irreducible factors      34
Irregular LDPC code, record performance      3
Iterative belief propagation algorithm, message passing      163
Iterative belief propagation decoding      162
Iterative bit-flip decoding      161
Iterative decoding convergence      152
Key equation      47
LDPC code      159
LDPC code, error detection capability      166
Likelihood      85
Linear code as vector subspace      6
Linear feedback shift-register (LFSR)      49
List decoding      134
Log and antilog tables      42
Log-likelihood metric      122
Log-likelihood ratio (LLR)      145
Log-likelihood ratio (LLR), extrinsic      146
Log-MAP algorithm      139
Low-density parity-check code      159
MacWilliams identity      56
MAP algorithm      137
Massey algorithm      63
Matrix, generator and parity—check      6
Matrix, Vandermonde      45
Max-Log-MAP algorithm      140
Maximum-a-posteriori probability      137
Maximum-distance-separable (MDS) code      62
Maximum-distance-separable (MDS) code, weight distribution      71
Maximum—length sequence (MLS) code      37
Meggit decoder      39
Message passing      163
Metric normalization      90
Metric, log-likelihood      122
Minimal polynomial      43
Minimum Hamming distance      4
Minimum squared Euclidean distance      173
MLD decoding      175
MLD decoding, defined      15
MLD decoding, Viterbi algorithm      86
Modified Forney syndrome      67
Modified syndrome polynomial      67
Modulation as mapping      170
Monte Carlo integration      19
MSED      173
Multilevel coding      180
Multilevel modulation code, definition      181
Multistage decoding      182
Natural labeling      174
Non-primitive BCH codes      38
Non-systematic cyclic code      35
Nyquist bandwidth      169
Order of an element in $GF(2^m)$      43
Ordered statistics decoding      131
Orthogonal checks      30
Outer code      110
Parallel concatenated code      147
Parallel decoding of multilevel codes      185
Parity node      159
Parity sub-matrix      7
Parity-check matrix      6
Parity-check matrix of BCH code      45
Parity-check matrix of cyclic code      36
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 code      27 45
Polynomial, associated with vector      33
Polynomial, erasure locator      67
Polynomial, errata locator      68
Polynomial, error      46
Polynomial, error evaluator      62
Polynomial, error locator      47
Polynomial, generator      34
Polynomial, minimal      43
Polynomial, modified syndrome      67
Polynomial, parity-check      36
Polynomial, primitive      41
Polynomial, syndrome      39
Primitive, element      41
Primitive, polynomial      41
Probability, a-posteriori      135
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