Algebraic decoding for doubly cyclic convolutional codes

Heide Gluesing-Luerssen; Uwe Helmke; José Ignacio Iglesias Curto

doi:10.3934/amc.2010.4.83

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2010, Volume 4, Issue 1: 83-99. Doi: 10.3934/amc.2010.4.83

This issue Previous Article On linear equivalence and Phelps codes Next Article

Algebraic decoding for doubly cyclic convolutional codes

1.
Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027
2.
Institut für Mathematik; Lehrstuhl für Mathematik II, Universität Würzburg, Am Hubland, 97074 Würzburg,
3.
Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca

Received: July 31, 2009

Revised: October 31, 2009

Published: January 2010

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Abstract

An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be corrected. The algorithm can be efficiently used on a particular class of convolutional codes, known as doubly cyclic convolutional codes. Due to their highly algebraic structure those codes are well suited for the algorithm and the main step of the procedure can be carried out using Reed-Solomon decoding. Examples illustrate the decoding and a comparison with existing algorithms is made.

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Mathematics Subject Classification: Primary: 94B10, 94B35; Secondary: 93B15, 93B20.

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