2010/01/23 by Sagar Shenvi, Shenvi, Sagar, Bikash Kumar Dey +1
Computer Science · Engineering · #Advanced MIMO Systems Optimization #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1001.4137
openalex publication_date 2010/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a directed acyclic network with three sources and three terminals such that each source independently generates one symbol from a given field F and each terminal wants to receive the sum (over F) of the source symbols. Each link in the network is considered to be error-free and delay-free and can carry one symbol from the field in each use. We call such a network a 3-source 3-terminal \it (3s/3t) sum-network. In this paper, we give a necessary and sufficient condition for a 3s/3t sum-network to allow all the terminals to receive the sum of the source symbols over any field. Some lemmas provide interesting simpler sufficient conditions for the same. We show that linear codes are sufficient for this problem for 3s/3t though they are known to be insufficient for arbitrary number of sources and terminals. We further show that in most cases, such networks are solvable by simple XOR coding. We also prove a recent conjecture that if fractional coding is allowed, then the coding capacity of a 3s/3t sum-network is either 0,2/3 or ≥ 1.