Distance distribution of binary codes and the error probability of decoding

Authors:
A. Barg;A. McGregor
Affiliations:
Dept. of Electr. & Comput. Eng., Maryland Univ., College Park, MD, USA;-
Venue:
IEEE Transactions on Information Theory
Year:
2005

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Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing

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Abstract

We address the problem of bounding below the probability of error under maximum-likelihood decoding of a binary code with a known distance distribution used on a binary-symmetric channel (BSC). An improved upper bound is given for the maximum attainable exponent of this probability (the reliability function of the channel). In particular, we prove that the "random coding exponent" is the true value of the channel reliability for codes rate R in some interval immediately below the critical rate of the channel. An analogous result is obtained for the Gaussian channel.