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

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Alexander Barg, Andrew McGregor
• Keywords: Binarysymmetric Channel, CORR 2004, Education, Improved Upper Bound, Maximum Attainable Exponent