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| Wicker S.B., Kim S. — Fundamentals of Codes, Graphs, and Iterative Decoding |
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| Предметный указатель |
Gilbert bound 9
Gilbert — Varshamov bound 11 42 150
Gilbert, E.N. 211
Giotto 70
Glavieux, A. xvii 61 70 71 121 122 210
Golay codes xiv 51
Golay codes, extended 52
Golay codes, ternary 52
Golay, M. xiv
Gore, W.C 212
Gorenstein, D. 53 211
Gould, S.J. xiii
Graph theory xviii 12 79
Graph, adjacency matrix 82 177
Graph, bipartite 79 80 137 177
Graph, Cayley 87 148 174
Graph, chromatic number 80 86
Graph, clique 104
Graph, connected 96
Graph, directed 80
Graph, directed acyclic (DAG) 97
Graph, disconnected 80
Graph, edge-vertex incidence 79 81 92 148
Graph, eigenvalue 79 82 83 86 88 139
Graph, expander 79 83 175
Graph, expansion 139 142 143 184 187
Graph, high girth 173
Graph, irregular 80
Graph, junction tree 104
Graph, loopy 115
Graph, moral 95
Graph, multiply-connected 97
Graph, path-l-vertex incidence 92
Graph, polytree 97
Graph, Ramanujan 87 88 148—150 175 206
Graph, random 84
Graph, regular 79 80
Graph, singly-connected 97
Graph, tree 97
Graph, tree, equivalent 115
Graph, triangulated 105
Graph, unconnected 96
Graph, undirected 80
Greatest common divisors 18
Ground field 23
Guruswami, V. 205 208 212
Hagenauer, J. 212
Hamming, bound xiv 9
Hamming, codes xiv 44
Hamming, codes, extended 44
Hamming, distance 2
Hamming, R.W. xiv 39
Hammons, A.R., Jr. 211
Hard decision decoding 7
Head-to-head 98
Heckerman, D. 215
Heegard, C. xvii 212
High girth code 151
High girth graph 173
Hirasawa, S. 212
Hocquenghem, A. xv 53 212
Horn, G.B. 209
Huffman, W.C. xvi 216
Hungerford, T.W. 212
Ideals 13 37
Ideals, principle 37
Identity 14
Immink, Kees A.S. 212
Incidence function 178
Indyk, P. 205 208 212
Inequality, Azuma’s 156
Information node 177
Information, a priori 122 129
Information, extrinsic 122 129
Information, systematic 122 129
Inner code 61 68
Input-output weight enumerating function (IOWEF) 67
Input-redundancy weight enumerating function (IRWEF) 65
Intelsat 54
Interleaver, uniform 72
Inverses 14
Irreducible polynomials 28
Irregular graph 80
Iterative decoding xvii
Jacq, S. 214
Jelinek, F. xvi 209
Jensen, F.V. 212
Jin, H. 208 212
Joint entropy 3
Jordan, M.L 215
Junction tree 104
Junction tree propagation algorithm 93 104 106 108 112 114 115
Kahale, N. 92 212
Kasahara, E.M. 212
Khandekar, A. 212
Kim, S. 208 212
Komlos, J. 209
Kotter, R. 216
Kschischang, F.R. xvii 134 212
Lafferty, J. 174 213
Lagrange, Joseph Louis 16
Lagrange’s Theorem 16
Language recognition problem 5
Lauritzen, S.L. 212
Left coset 15
LeGoff, S. 213
Lengthened codes 42
Lidl, R. 13
Lin, Shu 213
Linear code 40
Linear independence 24
Linear programming 161 174
Lipschitz condition 85 86
Locator polynomial 55
Loeliger, H.-A. 213
Logarithmic cost model 6
Logical circuit, depth 6
Logical circuit, model 6
Logical circuit, size 6
Loop 97
Loopy graph 115
Loss recovery algorithm 197
Low-density generator code 12 177 179—181 187
Low-density generator code, irregular 178
Low-density generator code, regular 178
Low-density parity-check code 12 137 177 187
Low-density parity-check code, Bayesian network representation 164
Low-density parity-check code, decoding 143 151
Low-density parity-check code, decoding, belief propagation 162 164
Low-density parity-check code, regular 137
Lubotzky, A. 87 148 213
Luby, M. xviii 174 193 200 208 209
MacKay, D.J.C. xvii xviii 174 211
MacWilliams, F.J. 214
Margulis, G.A. 87 148 173 214
Markov random field 95 99
Martingale 79 83 155 188
Martingale, edge exposure 84
Martingale, sequence 84 85 90
Martingale, vertex exposure 85 86
Mason’s gain rule 73
Massey, P.C 215
Mattson — Solomon polynomial 34
Maximum a posteriori (MAP) decoding 8
Maximum cardinality of a code 9
Maximum distance separable (MDS) 12
Maximum likelihood decoding 8 112 113 115
Maximum likelihood sequence decoding xv
McEliece — Rodemich — Rumsey — Welch bound 11
McEliece, R.J. xvii 13 77 134 196 207 209 214
| Memory vector 63
Memoryless channel 1
Message 102
Message-passing algorithm 93 103 115—118 120
Miller, G. 210
Minimal polynomial 13 28
Minimal polynomial, roots 30
Minimum distance 2
Minimum distance, linear block code 40
Minimum relative distance 10
Minty, G.J. xvi
Mitzenmacher, M. xviii 213
Montorsi, G. 77 132 210
Moral graph 95
Motwani, R. 214
Muller, D. xiv 45
Multiply-connected graph 97
Mutual information 3
Namekawa, T. 212
Naor, J. 209
Naor, M. 209
Narrow-sense BCH codes 55
National Aeronautics and Space Agency (NASA) 70
Neal, R.M. 213
Nearest-codeword decoding 7
Niederreiter, H. 13
Node degree sequence 138
Noisy Channel Coding Theorem xiii 3 4
Nondeterministic algorithm 5
Nonsystematic convolutional encoders 63
NP-complete 6
NP-hard 6 172
Offer, E 212
Olesen, K.G. 212
Order, Galois field element 21
Order, group element 15
Order, q modulo n 33
Oswald, P. 208 214
Outer code 61 68
Papke, L. 212
Parallel concatenated code 70 71 123
Parallel concatenated code, encoding xvii 61 70
Parent 97
Parity check matrix 41
Parity relations xiv
Parity-check codes 44
Path-l-vertex incidence graph 92
Pearl, J. 100 214
Perez, L.C 132 214
Perfect codes 9 52
Peterson, W.W. 53 214
PGL(2, Z/qZ) 87
Phillips, R. 87 148 213
Picart, A. 214
Pinsker, M.S. 173 216
Pippenger, N. 214
Planetary standard 69
Pless, V. xvi 216
Pollara, R 210
Polynomial time complexity 5
Polynomial, code 49
Polynomial, generator 50
Polynomial, irreducible 28
Polynomial, locator 55
Polynomial, matrix 64
Polynomial, Mattson — Solomon 34
Polynomial, minimal 28
Polynomial, primitive 28
Polynomial, spectrum 36
Polytree 97
Prange, G. xv
Primitive BCH codes 55
Primitive element 23
Primitive polynomial 28
Primitive roots 32
Principle ideal 37
Probabilistic independence network 95
Probabilistic reasoning 93 94 99 100 104 106
Probability model 94
Product codes 58
Product codes, cyclic 58
Projective general linear group 87
Punctuated equilibrium model xiii
Punctured codes 42
Pyndiah, R. 214
Quadratic residue 50
Quadratic residue, codes 51
Raghavan, P. 214
Ramanujan graph 87 88 148—150 175 206
Ramanujan, Srinivasa Aiyangar 87
Random access machine (RAM) 6
Random graph 84
Rate, achievable 2
Rate, code 40
Raviv, J. xvi 209
Ray-Chaudhuri, D.K. xv 53 210
Recursive constructions 40
Recursive convolutional encoders 63
Recursive systematic convolutional encoders 66
Recursive systematic encoders 71
Redundancy 2
Reed — Muller codes xiv 45
Reed — Solomon codes xv 13 53 57 69
Reed — Solomon codes, extended 57
Reed — Solomon codes, minimum distance 57
Reed, I.S. xiv 45 54 215
Regular graph 79 80
Regular low-density parity-check code 137
Repeat-accumulate code 12 196
Repetition codes 43
Richardson, T. xviii 174 210
Right coset 15
Right regular degree sequence 195
Ring 16
Rockmore, D.N. 174 213
Rodemich, E.R. 11 214
Roots, minimal polynomial 30
Roots, primitive polynomial 32
Rosenthal, J. 215
Roth, R. 209
Rumsey, H.C., Jr. 11 214
Rusmevichientong, P. 215
Sakk, Eric 215
Sarnak, P. 87 148 213
Satisfied constraint 143
Scalar field 23
Scalar multiplication 23
Seghers, J. 214
Semigroups 13
Semiring 17
Separation theorem 99
Sequential decoding xv
Set 13
Shannon limit xvii 39 71 79 175
Shannon, C.E. 1 61 121 215
Sharp concentration theorem 155 157—159 163 169
Shimony, S.E. 215
Shokrollahi, M.A. xviii 191 194 195 208 213
Shortened codes 42
Simple tree 97
Singleton bound 57 150
Singleton upper bound 11
Singly-connected graph 97
Sipser, M. xviii 143 148 174 215
Sloane, Neil J.A. 214
Smyth, P. 215
Soft decision decoding 8
Solomon, G. xv 54
Spanning set 24
Spectral method 83
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