Title: Convolutional codes from group rings

Authors: Jessica OShaughnessy

Addresses: Department of Mathematical Sciences, Shenandoah University, Winchester, VA 22601, USA; School of Mathematics, Statistics, and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland

Abstract: Convolutional codes have been widely used and studied. Many of the best current convolutional codes have been found through computer search. However, constructing these codes by algebraic means will allow bigger codes to be found while maintaining high speed and low memory. Units in the group ring have been used to construct convolutional codes. These have been used to construct several known codes and several new codes. These known constructions are extended to a new construction. This new construction allows for calculations of lower bounds of the free distances produced by some types of generators. It is shown that all (2, 1) systematic convolutional codes may be constructed using group rings with the new construction. The new construction is hoped be used to find new convolutional codes that would allow for less storage requirements for larger codes. This may be extended to consider LDPC convolutional codes and turbo codes.

Keywords: group rings; group ring codes; free distance; systematic convolutional codes; group ring convolutional codes; algebraic constructions; group ring matrices.

DOI: 10.1504/IJICOT.2014.066083

International Journal of Information and Coding Theory, 2014 Vol.2 No.4, pp.171 - 190

Received: 19 Feb 2013
Accepted: 22 Mar 2014

Published online: 24 Nov 2014 *

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