2009/01/15 by Brijesh Kumar, Brijesh Kumar Rai, Rai, Brijesh Kumar +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0901.2198
arxiv created 2009/01/15 · openalex publication_date 2009/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider directed acyclic \em sum-networks with m sources and n terminals where the sources generate symbols from an arbitrary alphabet field F, and the terminals need to recover the sum of the sources over F. We show that for any co-finite set of primes, there is a sum-network which is solvable only over fields of characteristics belonging to that set. We further construct a sum-network where a scalar solution exists over all fields other than the binary field F2. We also show that a sum-network is solvable over a field if and only if its reverse network is solvable over the same field.