Wicker S.B., Kim S. — Fundamentals of Codes, Graphs, and Iterative Decoding :: Электронная библиотека попечительского совета мехмата МГУ

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Wicker S.B., Kim S. — Fundamentals of Codes, Graphs, and Iterative Decoding

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Название: Fundamentals of Codes, Graphs, and Iterative Decoding

Авторы: Wicker S.B., Kim S.

Аннотация:

Written for professionals and academicians working in the field of communications, this work explains how to exploit simple structural descriptions when designing codes. After an overview of Shannon theory and complexity theory, chapters overview classical error control coding, with an introduction to abstract algebra and block and convolutional codes. Later chapters review research of the 1990s and early 2000s and introduce graph theory. The book can be used for a graduate course. Wicker is affiliated with Cornell University; Kim, with the Korea Institute for Advanced Study.

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Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 224

Добавлена в каталог: 28.02.2007

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Предметный указатель

$(d_{v_1}, d_{v_2}, \alpha,\beta)$ expander      83
$(\alpha,\beta)$ expander      83
(n, k, d) code      2
a priori information      122 129
Abelian      14
Abstract algebra      12
Achievable rate      2
Additive white Gaussian noise channel      169
Adjacency matrix      82 137 177
Aji, S. M.      209
Ajtai, M.      92 209
Albanese, A.      209
Algebraic block codes      12a
Algebraic coding theory      12
Algorithm, BCJR      94 112 113 115
Algorithm, belief propagation      93 99 103 104 109 112
Algorithm, Berlekamp’s      xv
Algorithm, error reducing      182 183
Algorithm, Euclid’s      18
Algorithm, exponential time      5
Algorithm, Gallager      151—153 181 187
Algorithm, junction tree propagation      93 104 106 108 112 114 115
Algorithm, loss recovery      197
Algorithm, message-passing      93 103 115—118 120
Algorithm, nondeterministic      5
Algorithm, polynomial time      5
Algorithm, probabilistic reasoning      93 99 100 104 106
Algorithm, Viterbi      94 112 113
Alon, N.      87 174 209
Ancestor      97
Ancestor set      97
AND-ORtree      188
Associativity      14
Asymptotic behavior, function      5
Asymptotically good code      147 174
Augmented codes      42
Azuma’s inequality      85 86 90 156
Bahl, L. R.      xvi 209
Barg, A.      147 150 174 210
Basis      24
Baum — Welch algorithm      xvi
Baum, L.      xvi
Bayesian network      95 99 123
Bayesian network, low-density parity-check code      164
BCH bound      54 57
BCH codes      xv 53
BCH codes, design procedure      56
BCH codes, narrow-sense      55
BCH codes, primitive      55
BCJR algorithm      94 112 113 115
Belief propagation      xvii xviii 12 93 99 103 104 109 112 123 162 174
Benedetto, S.      77 132 210
Berger, T.      xix
Berlekamp, E. R.      210
Berlekamp’s algorithm      xv 13
Berrou, C.      xvii 61 70 71 121 122 210
Bethe free energy      117
Bhargava, V. K.      xv 212
Binary erasure channel (BEC)      4
Binary symmetric channel (BSC)      4 169
Bipartite graph      79 80 137 177
Blomer, J.      209
Boolean function      xiv 46
Boolean net function language      45
Bose, R. C.      xv 53 210
Bound, BCH      54 57
Bound, Gilbert      9
Bound, Gilbert — Varshamov      11 42 150
Bound, Hamming      9
Bound, McEliece — Rodemich — Rumsey — Welch      11
Bound, Singleton      11 57 150
Bound, sphere packing      9
Bounded distance decoding      7
Bruck, J.      209
Burshtein, D.      210
Capacity      61
Cardinality      13
Cascaded code      200 202
Cascaded code, decoding      201
Cascaded code, Spielman’s construction      202
Cauchy — Schwarz inequality      89
Cayley graph      87 148 174
CCSDS standard for deep space telemetry      61
Cellular telephony      61
Channel capacity      4
Characteristic      26
Check node      177
Check node, confused      186
Check node, unhelpful      186
Cheng, J.-F.      xvii 207 210
Child      97
Chinese remainder theorem      58
Chord      105
Chromatic number      80 86
Chung, R R. K.      209
Chung, S. Y.      210
Class NP      5
CLIQUE      104
Clique graph      104
Closure      14
Cocke, J.      xvi 209
Code polynomial      49
Code, asymptotically good      11 147 174
Code, augmented      42
Code, BCH      53
Code, cascaded      200 202
Code, cascaded, decoding      201
Code, cascaded, Spielman’s construction      202
Code, component      123
Code, concatenated      12 61 68 147
Code, construction      6
Code, convolutional      12 61 65
Code, cyclic      13 49
Code, decoding      6
Code, dimension      40
Code, encoding      6
Code, error reducing      181
Code, expander      174
Code, expurgated      42
Code, extended      42
Code, Golay      39 51
Code, Hamming      44
Code, Hamming, duals      47
Code, high girth      151
Code, inner      61
Code, lengthened      42
Code, low-density generator      12 177 179—181 187
Code, low-density generator, irregular      178
Code, low-density generator, regular      178
Code, low-density parity-check      12 137 177 187
Code, low-density parity-check, Bayesian network representation      164
Code, maximum cardinality      9
Code, maximum distance separable (MDS)      12
Code, outer      61
Code, parallel concatenated      71
Code, parity-check      44
Code, perfect      9 52
Code, product      58
Code, punctured      42
Code, quadratic residue      51
Code, rate      40
Code, Reed — Muller      39 45
Code, Reed — Muller, duals      47
Code, Reed — Solomon      13 39 53 57 69
Code, repeat-accumulate      12 196
Code, repetition      43
Code, shortened      42
Code, systematic      180
Code, tornado      193
Codeword      2

Codeword, finite      71
Codeword, node      137
Collins, O.M.      xvi 215
Common divisors      18
Commutative      14
complexity      5
Component code      68 123
Component encoder      xvii 70
Concatenated code      12 61 147
Concatenated code, serial      61
Conditional entropy      3
Confused      186
Conjugacy class      29
Conjugates of field elements      29
Connected graph      96
Constraint, length      63
Constraint, node      137
Constraint, node, degree      138
Constraint, satisfied      143
Constraint, unsatisfied      143
Consultative Committee for Space Data Systems (CCSDS)      68
Convolutional code      12 61 65
Convolutional encoder      62
Convolutional encoder, nonrecursive      62
Convolutional encoder, nonsystematic      63
Convolutional encoder, systematic      63
Cooper, G.F.      210
Coset      15
Coset, cyclotomic      33
Costello, D.J., Jr.      214
Cover, Thomas M.      211
Cyclic codes      xv 13 49
Cyclic graph      96
Cyclic product code      58
Cyclotomic cosets      33
D transform      63
D-Separation      98
Dagum, P.      211
Davey, M.C.      xviii 174 211
Decoding      2 6
Decoding, belief propagation      162
Decoding, belief propagation, low-density parity-check code      164
Decoding, bounded distance      7
Decoding, Gallager, performance      157
Decoding, hard decision      7
Decoding, low-density parity-check code      143 151
Decoding, maximum a posteriori (MAP)      8
Decoding, maximum likelihood      8 112 113 115
Decoding, nearest-codeword      7
Decoding, soft decision      8
Decoding, symbol-by-symbol MAP      8
Decoding, turbo      125
Decoding, Viterbi      69
Deep space telecommunications, xvi      39
Degree sequence      174 188
Degree sequence, irregular code, good      170
Degree sequence, node      138
Degree sequence, right regular      195
Degree, constraint node      138
Degree, variable node      138
Degree, vertex      80
Depth, logical circuit      6
descendent      97
Designed distance      55
Digital audio      39
Dimension Theorem      26
Dimension, code      40
Dimension, vector space      24
Directed Acyclic Graph (DAG)      97
Directed graph      80 95
Disconnected graph      80
Discrete channel      1
Discrete memoryless channel      1
Distributive law      16
Divsalar, D.      77 210
Dolinar, S.      211
Double cover      81 88
Dual space      25
Edge exposure martingale      84
Edge-vertex incidence graph      79 81 92 148
Edmonds, J.      209
Effective free distance      77
Eigenvalue      79 82 83 86 88
Eigenvalue, graph      139
El Gamal, H.      211
Eldridge, N.      xiii
Elias, P.      xv 61 211
Encoders, component      70
Encoders, convolutional      62
Encoders, parallel concatenated      70
Encoders, recursive convolutional      63
Encoders, recursive systematic      66 71
Encoding      6
entropy      3
Entropy, conditional      3
Entropy, joint      3
Equivalent tree      115
Error reducing algorithm      182 183
Error reducing code      181
Euclidean Domain      17
Euclid’s algorithm      18
Euclid’s algorithm, extended form      20
Euler $\phi$ function      22
European Space Agency (ESA)      70
evidence      100
Expander code      174
Expander graph      79 83 175
expansion      79 139 142 143 184 187
Expansion, bound      83
Expectation-Maximization (EM) algorithms      xvii
Explaining away      98
Exponential time complexity      5
Expurgated codes      42
Extended codes      42
Extended form of Euclid’s algorithm      20
Extended Hamming codes      44
Extended Reed — Solomon codes      57
Extrinsic information      122 129
Factoring       33
Fano      xv
Field      20
Field, Galois      21
Field, Galois, order       26
Field, Galois, order p      21
Fine, T.      xix
Finite codewords      71
Forney, G.D., Jr.      xvi 61 115 147 210 211
Fraction of errors      144
Fractional rate loss      62
Freeman, W.T.      216
Frey, B.      xvii 134 211
Function, Euler $\phi$       22
Function, incidence      178
Galileo      70
Gallager, R.G.      xviii 12 137 151 173 174 211
Gallager, R.G., decoding algorithms      151—153 181 187
Gallager, R.G., decoding algorithms, performance      157
Galois field      13 21
Galois field, Fourier transform      34
Galois field, Fourier transform, transform pair      34
Galois field, multiplicative structure      22
Galois field, order       26
Galois field, order p      21
Galois field, primitive element      23
Galois, Evariste      21
Gaussian approximation      174
Generator matrix      40
Generator matrix, convolutional code      64
Generator polynomial      50
Generator sequence      63

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