Multiple-bases belief-propagation decoding of high-density cyclic codes

Authors:
Thorsten Hehn;Johannes B. Huber;Olgica Milenkovic;Stefan Laendner
Affiliations:
Institute for Information Transmission, FAU Erlangen-Nuremberg, Germany;Institute for Information Transmission, FAU Erlangen-Nuremberg, Germany;Department of Electrical and Computer Engineering, University of Illinois at Urbana-hampaign;Institute for Information Transmission, FAU Erlangen-Nuremberg, Germany
Venue:
IEEE Transactions on Communications
Year:
2010

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Abstract

We introduce a new method for decoding short and moderate-length linear block codes with dense parity-check matrix representations of cyclic form. This approach is termed multiple-bases belief-propagation. The proposed iterative scheme makes use of the fact that a code has many structurally diverse parity-check matrices, capable of detecting different error patterns. We show that this inherent code property leads to decoding algorithms with significantly better performance when compared to standard belief-propagation decoding. Furthermore, we describe how to choose sets of parity-check matrices of cyclic form amenable for multiple-bases decoding, based on analytical studies performed for the binary erasure channel. For several cyclic and extended cyclic codes, the multiple-bases belief-propagation decoding performance can be shown to closely follow that of the maximum-likelihood decoder.