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Springer eBooks

Suboptimal Decoding of Linear Codes

Ilya I. Dumer

Published Jan 1, 1993• 9 citations
Publisher
DOI
10.1007/978-3-7091-2786-5_31

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Suboptimal decoding of linear codes in "symmetric" memoryless channels is considered. For the q-ary codes of length n /spl rarr/ /spl infin/ and code rate R the number of decoding operations is upper bounded by the value q/sup n(c+o(1)), where o(1) /spl rarr/ 0 and c = min(R(1 - R), (1 - R)/2). The decoding error probability /spl epsi/ is upper bounded by the double error probability /spl epsi//sub e/ of maximum likelihood (ML) decoding, while /spl epsi/ /spl sim/ /spl epsi//sub e/, when n /spl rarr/ /spl infin/. For the channels with discrete (quantified) output the better estimate c = R(1 - R)/(1 + R) is obtained.

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An efficient maximum-likelihood soft-decision decoding algorithm for linear block codes using a generalized Dijkstra's algorithm was proposed by Han, Hartmann, and Chen (1993). We prove that this algorithm is efficient for most practical communication systems where the probability of error is less than 10/sup -3/ by finding an upper bound of the computational effort of the algorithm. A suboptimal decoding algorithm is also proposed. The performance of this suboptimal decoding algorithm is within 0.25 dB of the performance of an optimal decoding algorithm for the (104, 52) binary extended quadratic residue code, and within 0.5 dB of the optimal performance for the (128, 64) binary BCH code, respectively.
Suboptimal decoding of linear codes in "symmetric" memoryless channels is considered. For the q-ary codes of length n /spl rarr/ /spl infin/ and code rate R the number of decoding operations is upper bounded by the value q/sup n(c+o(1)), where o(1) /spl rarr/ 0 and c = min(R(1 - R), (1 - R)/2). The decoding error probability /spl epsi/ is upper bounded by the double error probability /spl epsi//sub e/ of maximum likelihood (ML) decoding, while /spl epsi/ /spl sim/ /spl epsi//sub e/, when n /spl rarr/ /spl infin/. For the channels with discrete (quantified) output the better estimate c = R(1 - R)/(1 + R) is obtained.