Distance distribution of binary codes and the error probability of decoding

Details Distance distribution of binary codes and the error probability of decoding Distance distribution of binary codes and the error probability of decoding

2004-07-04

arxiv.org/abs/cs/0407011v3

IEEE Transactions on Information Theory vol. 51, no. 12, pp. 4237-4246 (2005).

Computer Science

Information Theory

16 pages, 3 figures. Submitted to IEEE Transactions on Information Theory. The revision was done for a final journal version (

Scientific paper

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. 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 code rate $R$ in some interval immediately below the critical rate of the channel. An analogous result is obtained for the Gaussian channel.

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