Skip to main content

Error Recovery Properties and Soft Decoding of Quasi-Arithmetic Codes

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.

Publisher note

To access the full article, please see PDF.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Simon Malinowski.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Malinowski, S., Jégou, H. & Guillemot, C. Error Recovery Properties and Soft Decoding of Quasi-Arithmetic Codes. EURASIP J. Adv. Signal Process. 2008, 752840 (2007). https://doi.org/10.1155/2008/752840

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

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

Keywords

  • Entropy
  • Information Technology
  • Quantum Information
  • Time Instant
  • Average Amount