2013/08/09 by Pirita Paajanen, Paajanen, Pirita
Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #Information Theory (cs.IT) #Structural Response to Dynamic Loads #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1308.2069
openalex publication_date 2013/08/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this paper we study the capacity/entropy region of finite, directed,\nacyclic, multiple-sources, multiple-sinks network by means of group theory and\nentropy vectors coming from groups. There is a one-to-one correspondence\nbetween the entropy vector of a collection of n random variables and a certain\ngroup-characterizable vector obtained from a finite group and n of its\nsubgroups. We are looking at nilpotent group characterizable entropy vectors\nand show that they are all also Abelian group characterizable, and hence they\nsatisfy the Ingleton inequality. It is known that not all entropic vectors can\nbe obtained from Abelian groups, so our result implies that in order to get\nmore exotic entropic vectors, one has to go at least to soluble groups or\nlarger nilpotency classes. The result also implies that Ingleton inequality is\nsatisfied by nilpotent groups of bounded class, depending on the order of the\ngroup.\n