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Systems engineering and electronics

Efficient decoding implementations of LDPC codes

Wenbo Wang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

As for the sum-product decoding algorithm of LDPC codes,a new kind of difference-based decoding method is proposed.The main idea about it is that the messages passed on the bipartite graph of LDPC are based on the probability differences,and the renewal of both check nodes and message nodes is carried out on the special addition domain.As for the renewal of check nodes,some differences possessing the minimum absolute values can be selected to further reduce the complexity of computation.In contrast with the traditional LLR-based decoding method,the proposed method has much lower complexity,while it has no obvious loss of performance and convergence.

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As for the sum-product decoding algorithm of LDPC codes,a new kind of difference-based decoding method is proposed.The main idea about it is that the messages passed on the bipartite graph of LDPC are based on the probability differences,and the renewal of both check nodes and message nodes is carried out on the special addition domain.As for the renewal of check nodes,some differences possessing the minimum absolute values can be selected to further reduce the complexity of computation.In contrast with the traditional LLR-based decoding method,the proposed method has much lower complexity,while it has no obvious loss of performance and convergence.
As for the sum-product decoding algorithm of low density parity check(LDPC) codes,a difference-based decoding method is proposed.The main idea is shown as follows: the messages passed on the bipartite graph of LDPC are based on the probability differences,and the updates of both check nodes and message nodes are carried out on some special addition domain.As for the update of check nodes,only some lowest differences can be selected for reducing computational complexity.In contrast with the traditional log-likelyhood-ratio-based(LLR-based) decoding method,the proposed method has much lower complexity,while it has no obvious loss of performance and convergence.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.
Reduced-Complexity Decoding of LDPC Codes 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 representation 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 a performance, latency, computational complexity, and memory-requirement perspective.
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.
As for the problems of the high complexity of Log-Domain sum-product LDPC decoding algorithm and the slow convergence rate based on SMP scheduling,this paper propose the simplified difference -domain LDPC decoding algorithm based on RMP scheduling.The update of variable-nodes are optimized by RMP scheduling,which can accelerate the convergence rate one time.Due to that the messages pass on the Tanner graph are probability differences and the update of check-nodes are carried out by w minimum absolute values,which can further reduce the complexity of computation.In contrast with decoding algorithm by experiment show that the proposed algorithm can reduce the complexity of computation and accelerate the convergence rate,while it has no obvious loss of decoding performance.