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Jayant Apte

Publications and source records attributed to Jayant Apte.

2 recordsLinked to original sources
arXiv2017

Explicit Polyhedral Bounds on Network Coding Rate Regions via Entropy Function Region: Algorithms, Symmetry, and Computation

Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded networks, distributed storage systems, and caching systems, can be posed as polyhedral projections. These problems are demonstrated to exhibit multiple types of polyhedral symmetries. It is shown how these symmetries can be exploited to reduce the complexity of solving these problems through polyhedral projection.

cs.IT↗
arXiv2017

Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding

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.

cs.IT↗