2008/03/07 by Tal Philosof, Philosof, Tal, Ram Zamir +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #DNA and Biological Computing #F.2.2 #FOS: Computer and information sciences #I.2.7 #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0803.1120
23 pages, 5 figures
openalex publication_date 2008/03/07 · arxiv created 2008/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For general memoryless systems, the typical information theoretic solution - when exists - has a "single-letter" form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some single-letter distribution. Is that the form of the solution of any (information theoretic) problem? In fact, some counter examples are known. The most famous is the "two help one" problem: Korner and Marton showed that if we want to decode the modulo-two sum of two binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the "doubly-dirty" multiple access channel (MAC). Like the Korner-Marton problem, this is a multi-terminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference but the receiver is not aware of any part of it. We give an explicit solution for the capacity region of a binary version of the doubly-dirty MAC, demonstrate how the capacity region can be approached using a linear coding scheme, and prove that the "best known single-letter region" is strictly contained in it. We also state a conjecture regarding a similar rate loss of single letter characterization in the Gaussian case.