2014/06/11 by Shao‐Lun Huang, Shao-Lun Huang, Huang, Shao-Lun +2 · 1 citation
Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1406.2834
27 pages, submitted to IEEE Transactions on Information Theory
arxiv created 2014/06/11 · openalex publication_date 2014/06/11 · arxiv updated 2014/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many network information theory problems face the similar difficulty of single-letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a structure by assuming that the distributions of interest are close to each other. Under this assumption, the K-L divergence is reduced to the squared Euclidean metric in an Euclidean space. In addition, we construct the notion of coordinate and inner product, which will facilitate solving communication problems. We will present the application of this approach to the point-to-point channel, general broadcast channel, and the multiple access channel (MAC) with the common source. It can be shown that with this approach, information theory problems, such as the single-letterization, can be reduced to some linear algebra problems. Moreover, we show that for the general broadcast channel, transmitting the common message to receivers can be formulated as the trade-off between linear systems. We also provide an example to visualize this trade-off in a geometric way. Finally, for the MAC with the common source, we observe a coherent combining gain due to the cooperation between transmitters, and this gain can be quantified by applying our technique.