Transmission of correlated sources over a MAC: A Gaussian approximation-based analysis

The problem of separately encoding and subsequently transmitting correlated sources over a discrete memoryless multiple-access channel is revisited. In particular, we examine the sufficient conditions on the source and the channel under which there exists a n-length block code satisfying the condition that the error probability of reconstructing the discrete memoryless multiple source is no larger than some fixed constant ϵ > 0, or in short, ϵ-lossless transmission. We modify the decoding rule of Cover-El Gamal-Salehi and analyze the error probability using Gaussian approximations to derive a second-order generalization their sufficient condition for the ϵ-lossless transmission of the correlated sources.