2008/08/19 by Dinesh Krithivasan, Krithivasan, Dinesh, S. Sandeep Pradhan +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0808.2659
arxiv created 2008/08/19 · openalex publication_date 2008/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we consider a distributed source coding problem with a joint distortion criterion depending on the sources and the reconstruction. This includes as a special case the problem of computing a function of the sources to within some distortion and also the classic Slepian-Wolf problem, Berger-Tung problem, Wyner-Ziv problem, Yeung-Berger problem and the Ahlswede-Korner-Wyner problem. While the prevalent trend in information theory has been to prove achievability results using Shannon's random coding arguments, using structured random codes offer rate gains over unstructured random codes for many problems. Motivated by this, we present a new achievable rate-distortion region for this problem for discrete memoryless sources based on "good" structured random nested codes built over abelian groups. We demonstrate rate gains for this problem over traditional coding schemes using random unstructured codes. For certain sources and distortion functions, the new rate region is strictly bigger than the Berger-Tung rate region, which has been the best known achievable rate region for this problem till now. Further, there is no known unstructured random coding scheme that achieves these rate gains. Achievable performance limits for single-user source coding using abelian group codes are also obtained as parts of the proof of the main coding theorem. As a corollary, we also prove that nested linear codes achieve the Shannon rate-distortion bound in the single-user setting.