2008/11/03 by Brijesh Kumar, Brijesh Kumar Rai, Rai, Brijesh Kumar +4
Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0811.0285
5 pages, 3 figures
arxiv created 2008/11/03 · openalex publication_date 2008/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of communicating the sum of m sources to n terminals in a directed acyclic network. Recently, it was shown that for a network of unit capacity links with either m=2 or n=2, the sum of the sources can be communicated to the terminals if and only if every source-terminal pair is connected in the network. We show in this paper that for any finite set of primes, there exists a network where the sum of the sources can be communicated to the terminals only over finite fields of characteristic belonging to that set. As a corollary, this gives networks where the sum can not be communicated over any finite field even though every source is connected to every terminal.