2012/05/06 by Kumar Viswanatha, Viswanatha, Kumar, Emrah Akyol +3
Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Limits and Structures in Graph Theory #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1205.1173
arxiv created 2012/05/06 · openalex publication_date 2012/05/06 · arxiv updated 2012/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.