By Topic

Algebraic network coding: A new perspective

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Kumar K. R. Dinesh ; Department of Electrical Engineering, Indian Institute of Technology Madras, India ; Andrew Thangaraj

Algebraic criteria for existence of scalar linear network codes to satisfy a set of connection requirements has been discussed extensively by Koetter and Meacutedard. Solving for a network code is now known to be equivalent to solving a system of polynomial equations obtained by assigning variables to edges in the line graph of the network and computing a suitable transfer function. An alternative formulation for arriving at an equivalent system of polynomial equations is given in this paper based on the decomposition of the original network into trees, which we call ldquoinformation flow treesrdquo. The basic idea is to exploit the graph structure and assign variables suitably. Interestingly, the information flow tree approach results in only linear and degree-2 equations that can be simplified considerably in directed acyclic networks as shown in prior work. In this article, we provide an alternative derivation of the information flow tree approach that results in two further extensions to networks with cycles. The first extension is to flow acyclic solutions on any directed cyclic network. The second extension is to cyclic networks where all strongly connected components are simple cycles. Here the degree of the equations we are left to solve is limited to 4.

Published in:

2009 IEEE International Symposium on Information Theory

Date of Conference:

June 28 2009-July 3 2009