On Field Size and Success Probability in Network Coding
Olav Geil, Ryutaroh Matsumoto, Casper Thomsen
TL;DR
This paper uses algebraic geometry to determine the minimal field size for linear network coding feasibility and provides improved success probability estimates for random coding, considering monomial support in determinants.
Contribution
It introduces a method to find the smallest feasible field size and refines success probability estimates by analyzing monomials in determinants of Edmonds matrices.
Findings
Method to determine minimal field size for network coding
Enhanced success probability estimates for random linear network coding
Analysis of monomials in determinants of Edmonds matrices
Abstract
Using tools from algebraic geometry and Groebner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.
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