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IEICE Transactions on Communications

Multi-Stage Decoding Scheme with Post-Processing for LDPC Codes to Lower the Error Floors

Beomkyu Shin, Hosung Park, Jong‐Seon No, Habong Chung

Published Jan 1, 2011• 6 citations
Publisher

Abstract

In this letter, we propose a multi-stage decoding scheme with post-processing for low-density parity-check (LDPC) codes, which remedies the rapid performance degradation in the high signal-to-noise ratio (SNR) range known as error floor. In the proposed scheme, the unsuccessfully decoded words of the previous decoding stage are re-decoded by manipulating the received log-likelihood ratios (LLRs) of the properly selected variable nodes. Two effective criteria for selecting the probably erroneous variable nodes are also presented. Numerical results show that the proposed scheme can correct most of the unsuccessfully decoded words of the first stage having oscillatory behavior, which are regarded as a main cause of the error floor.

DOI
10.1587/transcom.e94.b.2375

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In this letter, we propose a multi-stage decoding scheme with post-processing for low-density parity-check (LDPC) codes, which remedies the rapid performance degradation in the high signal-to-noise ratio (SNR) range known as error floor. In the proposed scheme, the unsuccessfully decoded words of the previous decoding stage are re-decoded by manipulating the received log-likelihood ratios (LLRs) of the properly selected variable nodes. Two effective criteria for selecting the probably erroneous variable nodes are also presented. Numerical results show that the proposed scheme can correct most of the unsuccessfully decoded words of the first stage having oscillatory behavior, which are regarded as a main cause of the error floor.
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.
In this paper, a new decoding scheme is proposed to improve the error correcting performance of low-density parity-check (LDPC) codes in high signal-to-noise ratio (SNR) region by using post-processing. It behaves as follows: First, a conventional LDPC decoding is applied to received LDPC codewords one by one. Then, we count the number of word errors in a predetermined number of decoded codewords. If there is no word error, nothing needs to be done and we can move to the next group of codewords with no delay. Otherwise, we perform a proper post-processing which pro-ducesa new soft-valued codeword (this will befully explained in the main body of this paper) and then apply the conventional LDPC decoding to it again to recover the unsuccessfully decoded codewords. For the proposed decoding scheme, we adopt a simple product code structure which contains LDPC codes and simple algebraic codes as its horizontal and vertical codes, respectively. The decoding capability of the proposed decoding scheme is defined and analyzed using the parity-check matrices of vertical codes and, especially, the combined-decodability is derived for the case of single parity-check (SPC) codes and Hamming codes used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error correcting capability in high SNR region with little additional decoding complexity, compared with the conventional LDPC decoding scheme.
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.
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.
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.
In this paper, a hybrid decoding scheme is proposed to lower the error floor of low-density parity-check codes. With the observation that some error bits' LLR values oscillate throughout iterative decoding procedure, a "feedback BP" (FBP) decoding algorithm is presented as second-stage decoding cell to reduce the phenomena of oscillations. The hybrid decoding scheme, which consists LLR-BP decoding algorithm and FBP decoding algorithm, detects errors in the codewords obtained by using the parity check equations of LDPC codes. Simulation results show that the new decoding scheme exhibits a lower error floor than that of belief propagation decoding algorithm in the moderate and high SNR region.