2016/05/15 by Jayant Apte, Apte, Jayant, John MacLaren Walsh +1
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Technologies #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1605.04598
submitted to IEEE Transactions on Information Theory, (this version: corrected figure 9)
openalex publication_date 2016/05/15 · arxiv created 2017/02/01 · arxiv updated 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer to test whether a certain rate vector is achievable with vector linear network codes for a multi-source network coding instance and whether there exists a multi-linear secret sharing scheme achieving a specified information ratio for a given secret sharing instance are shown to be special cases of CLRP. Methods for solving CLRP built from group theoretic techniques for combinatorial generation are developed and described. These techniques form the core of an information theoretic achievability prover, an implementation accompanies the article, and several computational experiments with interesting instances of network coding and secret sharing demonstrating the utility of the method are provided.