A New Achievable Rate-Distortion Region for Distributed Source Coding

In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically large -- are used to derive achievability results. However, it was recently observed that in various multi-terminal communications scenarios, using random codes with constant finite blocklength may lead to improved achievable regions compared to the conventional approach. In other words, in some network communication scenarios, there is a finite optimal value in the blocklength of the randomly generated code used for distributed processing of information sources. Motivated by this, a coding scheme is proposed which consists of two codebook layers: i) the primary codebook which has constant finite blocklength, and ii) the secondary codebook whose blocklength is taken to be asymptotically large. The achievable region is analyzed in two steps. In the first step, a characterization of the achievable region is derived using information measures which are functions of multi-letter probability distributions. In the next step, a computable single-letter inner-bound to the achievable region is derived. It is shown through several examples that the resulting rate-distortion region is strictly larger than the Berger Tung achievable region.