On the exact decoding error probability exponent of the random coding on BSC

TL;DR

This paper derives the exact decoding error probability exponent for random coding over a binary symmetric channel, providing precise analysis of error rates in information transmission.

Contribution

It introduces a new approach to determine the exact error exponent using novel results on the distribution of sums of random variables.

Findings

Derived the exact decoding error probability exponent for BSC

Provided new probabilistic results on sums of random variables

Enhanced understanding of error rates in random coding schemes

Abstract

For the information transmission over a binary symmetric channel the random coding is used. The transmission of exponential number of messages is considered. The exact decoding error probability exponent is derived. The proof is based on the new results on the distribution of a certain sum of random variables.