Information spectrum approach to the source channel separation theorem

A source-channel separation theorem for a general channel has recently been shown by Aggrawal et al.[1]. This theorem states that if there exists a coding scheme that achieves a maximum distortion level d_max over a general channel W, then reliable communication can be accomplished over this channel at rates less than R(d_max), where R(·) is the rate distortion function of the source. The source, however, is essentially constrained to be discrete and memoryless (DMS). In this work we prove a stronger claim where the source is general, satisfying only a “sphere packing optimality” feature, and the channel is completely general. Furthermore, we show that if the channel satisfies the strong converse property as defined by Han & Verdú [2], then the same statement can be made with d_avg, the average distortion level, replacing d_max. Unlike the proofs in [1], we use information spectrum methods and the results can be quite easily extended to other situations.