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Low-Complexity Decoding Schemes for LDPC Codes Using Efficient Unreliable Path Search

양필웅

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

This dissertation contains the following contributions on the low-complexity decoding schemes of LDPC codes.• Two-stage decoding scheme for LDPC codes -A new stopping criterion for LDPC codes -A new decoding scheme for LDPC codes with unreliable path search • Parallel unreliable path search algorithm • Analysis of two-stage decoding schemes -Validity and complexity analysis First, a new two-stage decoding scheme for low-density parity check (LDPC) codes to lower the error-floor is proposed.The proposed decoding scheme consists of the conventional belief propagation (BP) decoding algorithm as the first-stage decoding and the re-decodings with manipulated log-likelihood ratios (LLRs) of variable nodes as the second-stage decoding.In the first-stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes is determined, which can be partly included in the small trapping sets.In the second-stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re-decoding trials.Each re-decoding i trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion.Secondly, the parallel unreliable path search algorithm is proposed for practical application to the proposed unreliable path search algorithm.In order to reduce the decoding delay and computational complexity, an efficient method for the search algorithm based on the parallel message-passing algorithm in the LDPC decoding is proposed.The parallel unreliable path search algorithm significantly reduces the additional complexity without extra hardware requirements.Finally, the validity and the complexity analysis of the proposed unreliable path search algorithm is presented.The proposed algorithm effectively finds the variable nodes in small trapping sets much more faster than the previous random selection method.Also, it is verified that the additional complexity of the parallel unreliable path search algorithm is less than that of one iteration of iterative decoders.

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This dissertation contains the following contributions on the low-complexity decoding schemes of LDPC codes.• Two-stage decoding scheme for LDPC codes -A new stopping criterion for LDPC codes -A new decoding scheme for LDPC codes with unreliable path search • Parallel unreliable path search algorithm • Analysis of two-stage decoding schemes -Validity and complexity analysis First, a new two-stage decoding scheme for low-density parity check (LDPC) codes to lower the error-floor is proposed.The proposed decoding scheme consists of the conventional belief propagation (BP) decoding algorithm as the first-stage decoding and the re-decodings with manipulated log-likelihood ratios (LLRs) of variable nodes as the second-stage decoding.In the first-stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes is determined, which can be partly included in the small trapping sets.In the second-stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re-decoding trials.Each re-decoding i trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion.Secondly, the parallel unreliable path search algorithm is proposed for practical application to the proposed unreliable path search algorithm.In order to reduce the decoding delay and computational complexity, an efficient method for the search algorithm based on the parallel message-passing algorithm in the LDPC decoding is proposed.The parallel unreliable path search algorithm significantly reduces the additional complexity without extra hardware requirements.Finally, the validity and the complexity analysis of the proposed unreliable path search algorithm is presented.The proposed algorithm effectively finds the variable nodes in small trapping sets much more faster than the previous random selection method.Also, it is verified that the additional complexity of the parallel unreliable path search algorithm is less than that of one iteration of iterative decoders.
A two-stage decoding algorithm to lower the error-floor for low-density parity-check (LDPC) codes is presented. An efficient stopping criterion is proposed to avoid unnecessary iterations in the first stage. If the stopping criterion is reached, the first stage decoding will be terminated and the second stage decoding will be started, where the unsuccessfully decoded words are re-decoded by manipulating the log-likelihood ratio (LLR) of two types of specifically selected variable nodes. Simulation results show that the proposed algorithm can effectively lower the error floor of LDPC codes while maintaining a low decoding 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.
In this study, the authors propose a new two‐stage decoding scheme for low‐density parity‐check codes to lower the error‐floor, which consists of the conventional belief propagation (BP) decoding algorithm as the first‐stage decoding and the re‐decodings with manipulated log‐likelihood ratios (LLRs) of variable nodes as the second‐stage decoding. In the first‐stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes are determined, which can be partly included in the small trapping sets. In the second‐stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re‐decoding trials. Each re‐decoding trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion. The parallel unreliable path search algorithm is also proposed for practical application of the proposed algorithm. Numerical results show that the proposed early stopping criteria and the proposed decoding algorithms for the second‐stage decoding can correct most of the unsuccessfully decoded codewords by the first‐stage decoding in the error‐floor region.
Low density parity-check (LDPC) codes are a class of linear block codes that are decoded by running belief propagation (BP) algorithm or log-likelihood ratio belief propagation (LLR-BP) over the factor graph of the code. One of the disadvantages of LDPC codes is the onset of an error floor at high values of signal to noise ratio caused by trapping sets. In this paper, we propose a two stage decoder to deal with different types of trapping sets. Oscillating trapping sets are taken care by the first stage of the decoder and the elementary trapping sets are handled by the second stage of the decoder. Simulation results on the regular PEG (504,252,3,6) code and the irregular PEG (1024,518,15,8) code shows that the proposed two stage decoder performs significantly better than the standard decoder.
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.
Low density parity-check (LDPC) codes are a class of linear block codes that are decoded by running belief propagation (BP) algorithm or log-likelihood ratio belief propagation (LLR-BP) over the factor graph of the code. One of the disadvantages of LDPC codes is the onset of an error floor at high values of signal to noise ratio caused by trapping sets. In this paper, we propose a two stage decoder to deal with different types of trapping sets. Oscillating trapping sets are taken care by the first stage of the decoder and the elementary trapping sets are handled by the second stage of the decoder. Simulation results on regular PEG (504,252,3,6) code shows that the proposed two stage decoder performs significantly better than the standard decoder.