Open Access

Error Recovery Properties and Soft Decoding of Quasi-Arithmetic Codes

EURASIP Journal on Advances in Signal Processing20072008:752840

https://doi.org/10.1155/2008/752840

Received: 4 October 2006

Accepted: 9 July 2007

Published: 17 July 2007

Abstract

This paper first introduces a new set of aggregated state models for soft-input decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that close-to-optimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF) of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols). The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to close-to-optimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol.

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Authors’ Affiliations

(1)
IRISA/University of Rennes, Campus de Beaulieu
(2)
IRISA/INRIA

Copyright

© Simon Malinowski et al 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.