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IEEE Transactions on Information Theory

Residual error rate of binary linear block codes (Corresp.)

Gérard Cohen, Philippe Godlewski

Published Jul 1, 1976• 0 citations
Publisher

Abstract

Transposing a computation of Mac Williams we derive an exact expression for, and a straightforward upper bound on, the residual error rate of a binary block code with a "standard" decoder. We also give series expansions for decoding error probability and residual error rates.
DOI
10.1109/tit.1976.1055587

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A coset representation of the bit error probabilities for binary linear block codes and arbitrary symmetric memoryless channels is derived. Such a representation leads to simple upper bounds on the bit error probabilities for code components expressed via 2n code spectra, where n is the code length, and to a "bounded distance decoding" algorithm. The performance of the algorithm is illustrated for the (23,12) Golay code and a particular channel having non-binary output alphabet where it attains a sub-optimum performance.
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