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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