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IEEE International Symposium on Information Theory (ISIT)

Near optimal reduced-complexity decoding algorithms for LDPC codes

J. Chen, Ajay Dholakia, Evangelos S. Eleftheriou, M.P.C. Fossorier, X.-Y. Hu

Published Jun 25, 2003• 21 citations
Publisher

Abstract

In this paper, two families of reduced-complexity algorithms for decoding low-density parity-check (LDPC) codes based on incorporating either a normalization or a correction term in the check-node update are presented. A simplified symbol-node update can also be used. Using simulations, it is shown that these simplified belief propagation (BP) approaches provide near optimum performance with different classes of LDPC codes.

DOI
10.1109/isit.2002.1023727

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In this paper, two families of reduced-complexity algorithms for decoding low-density parity-check (LDPC) codes based on incorporating either a normalization or a correction term in the check-node update are presented. A simplified symbol-node update can also be used. Using simulations, it is shown that these simplified belief propagation (BP) approaches provide near optimum performance with different classes of LDPC codes.
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Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
In this paper, an algorithm for low-density parity-check (LDPC) codes with reduced complexity is presented. The complexity reduction is achieved by calculating a linear function for updating the check nodes in each iteration, instead of an exponential and logarithmic function. The parameters of the linear function are optimized by density evolution. Simulation results show that there is nearly no loss in the performance by using this approximation compared to the exact calculation of the belief propagation decoding algorithm, even for very large block lengths.
Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normalization and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.