Error Control Coding: Fundamentals and ApplicationsCompletely updated to cover latest developments, this text provides a bridge between introductory courses in digitial communications and more advanced courses in information technology. It presents state-of-the-art control techniques. |
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Page 70
... coset leader , an erroneous decoding will result . This can be seen as follows . The error pattern x caused by the channel must be in some coset and under some nonzero code vector , say in the Ith coset and under the code vector v0 ...
... coset leader , an erroneous decoding will result . This can be seen as follows . The error pattern x caused by the channel must be in some coset and under some nonzero code vector , say in the Ith coset and under the code vector v0 ...
Page 71
... coset leader is chosen to have minimum weight in its coset , the decoding based on the standard array is the minimum distance decoding or MLD . Let a denote the number of coset leaders of weight i . The numbers α , α1 , . . . , ɑ , are ...
... coset leader is chosen to have minimum weight in its coset , the decoding based on the standard array is the minimum distance decoding or MLD . Let a denote the number of coset leaders of weight i . The numbers α , α1 , . . . , ɑ , are ...
Page 72
... coset have the same syndrome . The syndromes for different cosets are different . Proof . Consider the coset whose coset leader is e ,. A vector in this coset is the sum of e , and some code vector v , in C. The syndrome of this vector ...
... coset have the same syndrome . The syndromes for different cosets are different . Proof . Consider the coset whose coset leader is e ,. A vector in this coset is the sum of e , and some code vector v , in C. The syndrome of this vector ...
Contents
CODING FOR RELIABLE DIGITAL TRANSMISSION | 1 |
INTRODUCTION TO ALGEBRA | 15 |
LINEAR BLOCK CODES | 51 |
Copyright | |
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Other editions - View all
Error Control Coding: Fundamentals and Applications Shu Lin,Daniel J. Costello No preview available - 2004 |
Error Control Coding: Fundamentals and Applications Shu Lin,Daniel J. Costello No preview available - 2004 |
Common terms and phrases
a₁ b₁ BCH code binary block code buffer register burst of length bytes C₁ C₂ capable of correcting code of length code polynomial code vector code word computation constraint length convolutional codes coset cyclic code decoding circuit detected dfree dmin EG code encoder error burst error digit error pattern error probability error-correcting capability Example fewer errors go-back-N ARQ Hamming code Hence hybrid ARQ IEEE Trans information sequence input integer interleaved linear code metric minimal polynomial minimum distance multiplication n-tuple nonzero orthogonal check sums output parity parity-check digits parity-check matrix parity-check sums path polynomial g(X primitive polynomial received polynomial received sequence received vector receiver buffer retransmission round-trip delay S₁ self-orthogonal sequential decoding shown in Figure sums orthogonal syndrome bits syndrome register systematic code Table Theorem throughput transmitted Viterbi algorithm Viterbi decoding weight zero α² α³