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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Purser M. — Introduction to error-correcting codes |
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| Ïðåäìåòíûé óêàçàòåëü |
BCH codes, error correction of binary 53—58
BCH codes, error correction of nonbinary 58—59
BCH codes, examples of 51—52
BCH codes, minimum polynomials in 47—48
BCH codes, Reed — Solomon codes 59—67
BCH codes, roots of 48—51
Berlekamp — Massey algorithm 58 125—127
Binary erasure channel 6
Binary information units (bits) 96
Binary symmetric channel (BSC) 111
Binomial approximations 113—116
Bit strings 1—7
Block codes 7
Block codes and convolutional codes 91—93
Bose — Chaudhuri — Hocquenghem codes see "BCH codes"
BSC (binary symmetric channel) 111
Bursts, of errors 6—7
Capacity, of channel 110
Closed code 12
Code rate 8
Code(s) and error correction 3—5
Code(s), bit strings and 1—7
Code(s), block 7 91—93
Code(s), closed 12
Code(s), Golay 18 38
Code(s), immediate 97
Code(s), perfect 18—19
Code(s), Reed — Solomon 29 59—67
Code(s), repetition 18—19
Code(s), tree and trellis 69—72
Code-distance 7
Codevectors 3
Codewords 3
Columns, of null matrix 17—18
Constraint length 70
Convolutional codes, analysis of 78—81
Convolutional codes, block codes and 91—93
Convolutional codes, control of decoding errors with 77—78
Convolutional codes, defined 73
Convolutional codes, error correcting with 81—91
Convolutional codes, feedback decoding with 86—89
Convolutional codes, linear 72—78
Convolutional codes, sequential decoding with 85—86
Convolutional codes, soft-decision decoding with 84—85
Convolutional codes, syndrome decoding with 87—91
Convolutional codes, tree and trellis codes 69—72
Correlated sources 102—107
cosets 12
Cyclic codes, defined 32
Cyclic codes, error correction with 42—44
Cyclic codes, error detection with 38—42
Cyclic codes, generating polynomial for 31—35
Cyclic codes, nonbinary 44—46
Cyclic codes, roots of generating polynomial and null matrix in 35—37
Cyclic codes, shortened 40—42
Cyclic codes, systematic 33—35
Cyclic codes, weight distributions of 39—40
Decoding errors, control of 77—78
Decoding, feedback 86—89
Decoding, sequential 85—86
Decoding, soft-decision 5—7 84—85
Decoding, syndrome 89—91
Delay operator 76
Detectable errors 24—25
Distance, of linear code 17
entropy 96
Entropy of correlated source 102
Equivocation 108 111
Erasures 5—7
Error correction with binary BCH codes 53—58
Error correction with convolutional codes 81—91
Error correction with cyclic codes 42—44
Error correction with nonbinary BCH codes 58—59
Error correction, codes and 3—5
Error correction, forward 4
Error detection, with cyclic codes 38—42
Error locator 53
Error(s), bursts of 6—7
Error(s), detectable 24—25
Error(s), postdecoding 80—81
Error-recovery, by detection and retransmission 4
Feedback decoding, with convolutional codes 86—89
Feedback shift registers 40—42
Field(s) 117
| Field(s), finite 11 117—124
Forward error correction (FEC) 4
Generating polynomial 31—35
Generating polynomial, roots of, and null matrix 35—37
Generator matrix 13—14
Golay code 18 38
Hamming distance 7—8
Ideal 31
Immediate code 97
Information in transit 107—111
Information rate 107
Information theory, correlated sources in 102—107
Information theory, information in transit in 107—111
Information theory, information, entropy, redundancy, and compression in 95—102
Information units, binary 96
Information, associated with event 95—96
Information, average 96
Information, maximum 96—97
Information, mutual 109 111
Interleaved RS code 63—64
Kasami method 42—43
Linear codes, bounds in practice on 23—25
Linear codes, convolutional 72—78
Linear codes, distance of 17
Linear codes, matrix representation for 11—14
Linear codes, nonbinary 25—29
Linear codes, null matrix or parity-check matrix for 14—18
Linear codes, perfect codes in 18—19
Linear codes, Plotkin bound on 20—23
Linear codes, Varsharmov — Gilbert bound on 19—20
Matrix, generator 13—14
Matrix, null 14—18
Matrix, parity 13
Matrix, parity-check 14—18
Matrix, representation of 11—14
Metric 83
Minimum polynomials, in BCH codes 47—48
Minimum weight 12
Mutual information 109 111
Nonbinary BCH codes, error correction of 58—59
Nonbinary cyclic codes 44—46
Nonbinary linear codes 25—29
Null matrix 14—18
Null matrix, columns of 17—18
Null matrix, roots of generating polynomial and 35—37
NullSpace 14
Parity matrix 13
Parity-check matrix 14—18
Perfect codes 18—19
Plotkin bound 20—23
Postdecoding errors 80—81
Preamble 72
Redundancy 2—3 97
Reed — Solomon (RS) codes 29 59—67
Reed — Solomon (RS) codes, interleaved 63—64
Reed — Solomon (RS) codes, nearness to bounds of 65—67
Reed — Solomon (RS) codes, practical use of 62—64
Reed — Solomon (RS) codes, weight distribution of 64—65
Reed — Solomon (RS) codes, worked example of 60—62
Reliability factor 6
Repetition codes 18—19
Residual error rate 64
Retransmission, error-recovery by 4
Roots of BCH codes 48—51
Roots of cyclic codes 35—37
Roots, consecutive 48
RS codes see "Reed — Solomon (RS) codes"
Sequential decoding, with convolutional codes 85—86
Shannon's Theorem 8—10
Soft-decision decoding 5—7
Soft-decision decoding with convolutional codes 84—85
Sources, correlated 102—107
Sphere-packing 7—8
Standard array 12
subspace 12
Syndrome 15—17
Syndrome decoding, with convolutional codes 87—91
Tree codes 69—72
Trellis codes 69—72
Varsharmov — Gilbert bound 19—20
Viterbi algorithm 70—72
Weight distributions of cyclic codes 39—40
Weight distributions of Reed — Solomon code 64—65
Weight, of linear code 17
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