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International Conference on Communications and Networking in China (ChinaCom)

Lowering the Error Floor of LDPC Codes by a Two-stage Hybrid Decoding Algorithm

Yueguang Bian, Youzheng Wang, Jing Wang

Published Aug 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1109/chinacom.2007.4469460

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IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•4 citations
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.
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.
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.
Irregular Low-Density Parity-Check (LDPC) codes generally achieve better performance than regular LDPC codes at low E b /N 0 values. They have, however, higher error floors than regular LDPC codes. With respect to the construction of the irregular LDPC code, it can achieve the trade-off between the performance degradation of low E b /N 0 region and lowering error floor. It is known that a decoding algorithm can achieve very good performance if it combines the Ordered Statistic Decoding (OSD) algorithm and the Log Likelihood Ratio-Belief Propagation (LLR-BP) decoding algorithm. Unfortunately, all the codewords obtained by the OSD algorithm satisfy the parity check equation of the LDPC code. While we can not use the parity check equation of the LDPC code to stop the decoding process, the wrong codeword that satisfies the parity check equation raises the error floor. Once a codeword that satisfies the parity check equation is generated by the LLR-BP decoding algorithm, we regard that codeword as the final estimate and halt decoding; the OSD algorithm is not performed. In this paper, we propose a new encoding/decoding scheme to lower the error floor created by irregular LDPC codes. The proposed encoding scheme encodes information bits by Cyclic Redundancy Check (CRC) and LDPC code. The proposed decoding scheme, which consists of the LLR-BP decoding, CRC check, and OSD decoding, detects errors in the codewords obtained by the LLR-BP decoding algorithm and the OSD decoding algorithm using the parity check equations of LDPC codes and CRC. Computer simulations show that the proposed encoding/decoding scheme can lower the error floor of irregular LDPC codes.
In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high b/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.
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.