Distance distribution of binary codes and the error probability of decoding
<|reference_start|>Distance distribution of binary codes and the error probability of decoding: 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.<|reference_end|>
@article{barg2004distance,
    title={Distance distribution of binary codes and the error probability of
  decoding},
    author={Alexander Barg and Andrew McGregor},
    journal={IEEE Transactions on Information Theory vol. 51, no. 12, pp.
  4237-4246 (2005).},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0407011},
    primaryClass={cs.IT math.IT}
}