Network-error correcting codes using small fields

Prasad, Krishnan and Rajan, Sundar Sundar (2011) Network-error correcting codes using small fields. In: International Symposium on Information Theory (ISIT), July 31 2011-Aug. 5 2011, St. Petersburg, Russia.

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Abstract

Recently, Ebrahimi and Fragouli proposed an algorithm to construct scalar network codes using small fields (and vector network codes of small lengths) satisfying multicast constraints in a given single-source, acyclic network. The contribution of this paper is two fold. Primarily, we extend the scalar network coding algorithm of Ebrahimi and Fragouli (henceforth referred to as the EF algorithm) to block network-error correction. Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. We give an algorithm which, starting from a given network-error correcting code, can obtain another network code using a small field, with the same error correcting capability as the original code. Our secondary contribution is to improve the EF Algorithm itself. The major step in the EF algorithm is to find a least degree irreducible polynomial which is coprime to another large degree polynomial. We suggest an alternate method to compute this coprime polynomial, which is faster than the brute force method in the work of Ebrahimi and Fragouli.

Item Type:	Conference Proceedings
Publisher:	IEEE
Additional Information:	Copyright of this article belongs to IEEE.
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	02 Apr 2013 08:29
Last Modified:	02 Apr 2013 08:29
URI:	http://eprints.iisc.ac.in/id/eprint/46143

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