Computer Science > Information Theory
[Submitted on 8 Jul 2008 (v1), last revised 19 Jun 2010 (this version, v2)]
Title:Path Gain Algebraic Formulation for the Scalar Linear Network Coding Problem
View PDFAbstract:In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its demand to obtain polynomial equations. In this work, we propose a method to derive the polynomial equations using source-to-sink path gains as the variables. In the path gain formulation, we show that linear and quadratic equations suffice; therefore, network coding becomes equivalent to a system of polynomial equations of maximum degree 2. We present algorithms for generating the equations in the path gains and for converting path gain solutions to edge-to-edge gain solutions. Because of the low degree, simplification is readily possible for the system of equations obtained using path gains. Using small-sized network coding problems, we show that the path gain approach results in simpler equations and determines solvability of the problem in certain cases. On a larger network (with 87 nodes and 161 edges), we show how the path gain approach continues to provide deterministic solutions to some network coding problems.
Submission history
From: Abhay Trichur Subramanian [view email][v1] Tue, 8 Jul 2008 02:51:49 UTC (113 KB)
[v2] Sat, 19 Jun 2010 12:57:20 UTC (118 KB)
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