Finite blocklength bounds for multiple access channels with correlated sources

Refined bounds on the probability of decoding error for arbitrary multiple-access channels with correlated sources are derived. The contribution of this paper is to give new upper bounds on the probability of decoding error for any given blocklength. These bounds can be used for the analysis over any multiple-access channels with correlated and uncorrelated sources in the finite blocklength regime. It is shown that the derived bounds can recover previously known bounds for the multiple access channel with correlated and uncorrelated sources.