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IEEE International Symposium on Information Theory (ISIT)

Computational Performance of Various Formulations of the Iterative Soft-Decision Decoder Algorithm

Raymond Moberly, Michael E. O’Sullivan

Published Jul 1, 2006• 1 citation
Publisher

Abstract

Multiple formulations of the soft-decision decoding algorithm have been published based upon Gallagher's foundational work on LDPC codes (R. Gallager, 1962) and Pearl's iterative belief-propagation (1988). Three published formulations are mathematically identical but differ computationally. A formulation is proposed that is computationally better than the established ones. A visualization strategy is introduced to describe the formulations

DOI
10.1109/isit.2006.261645

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Multiple formulations of the soft-decision decoding algorithm have been published based upon Gallagher's foundational work on LDPC codes (R. Gallager, 1962) and Pearl's iterative belief-propagation (1988). Three published formulations are mathematically identical but differ computationally. A formulation is proposed that is computationally better than the established ones. A visualization strategy is introduced to describe the formulations
In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.
In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.
Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.