Subset Typicality Lemmas and Improved Achievable Regions in Multiterminal Source Coding

Consider the following information theoretic setup wherein independent codebooks of N correlated random variables are generated according to their respective marginals. The problem of determining the conditions on the rates of codebooks to ensure the existence of at least one codeword tuple which is jointly typical with respect to a given joint density (called the multivariate covering lemma) has been studied fairly well and the associated rate regions have found applications in several source coding scenarios. However, several multiterminal source coding applications, such as the general multi-user Gray-Wyner network, require joint typicality only within subsets of codewords transmitted. Motivated by such applications, we ask ourselves the conditions on the rates to ensure the existence of at least one codeword tuple which is jointly typical within subsets according to given per subset joint densities. This report focuses primarily on deriving a new achievable rate region for this problem which strictly improves upon the direct extension of the multivariate covering lemma, which has quite popularly been used in several earlier work. Towards proving this result, we derive two important results called `subset typicality lemmas' which can potentially have broader applicability in more general scenarios beyond what is considered in this report. We finally apply the results therein to derive a new achievable region for the general multi-user Gray-Wyner network

An Achievable Rate Region for Distributed Source Coding and Dispersive Information Routing

Abstract—This paper considers the problem of optimal multihop routing of correlated sources over a network with multiple sinks and arbitrary network demands. We recently introduced a new routing paradigm in [10] called ‘dispersive information routing ’ (DIR), wherein the intermediate nodes are allowed to split a packet and forward a subset of the received bits on each forward path. DIR ensures that each sink receives just the information it requires to decode the sources it intends to reconstruct, and thereby outperforms conventional routing techniques in the literature. We proposed an encoding scheme called ‘power binning ’ which achieves complete rate region and the minimum cost under this paradigm when each sink is allowed to receive packets only from the sources it wants to reconstruct. This paper considers the optimum encoding scheme when every source can (possibly) communicate with every sink irrespective of what the sinks reconstruct. This generalization happens to be considerably more complex and we derive an achievable rate region and an associated achievable cost using principles from distributed source coding and multiple descriptions encoding. Index Terms—Distributed source coding, joint compression and routing I