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Improved Perturbation Method for Decoding of LDPC Aided by CRC

Si Hui Shu, Daiming Qu

Published Jun 4, 2014• 2 citations
OpenAlex

Abstract

In this paper, a fresh belief propagation (BP) decoding algorithm is proposed. The proposed decoding algorithm with improved perturbation method is designed for short length low density parity-check (LDPC) codes aided by cyclic redundancy check (CRC). In the proposed algorithm corresponding to path size L, L decoding paths are considered concurrently. Then, a single codeword is selected according to the checking results of CRC. Simulation results show that the modified CRC-aided decoding scheme can enhance the error-correcting performance of short LDPC codes effectively.

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International Journal of Communication Systems•Feb 28, 2017•2 citations
In this paper, a fresh belief propagation (BP) decoding algorithm is proposed. The proposed decoding algorithm with improved perturbation method is designed for short length low density parity-check (LDPC) codes aided by cyclic redundancy check (CRC). In the proposed algorithm corresponding to path size L, L decoding paths are considered concurrently. Then, a single codeword is selected according to the checking results of CRC. Simulation results show that the modified CRC-aided decoding scheme can enhance the error-correcting performance of short LDPC codes effectively.
In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.
In modern communication systems, the concatenation of a low-density parity-check (LDPC) code with a cyclic redundancy check (CRC) code is commonly used for error correction. In this paper, we propose a low-complexity two-stage scheme for decoding these codes using their concatenation structures. In the first stage, the traditional belief propagation (BP)-based iterative algorithm with a relative small maximum number of iterations is performed for decoding the LDPC code. If an LDPC codeword is obtained in this stage, the decoding process terminates. Otherwise, the second stage of the decoding process is performed, in which the guessing random additive noise decoding (GRAND) algorithm is applied to the CRC code. A list of information sequences satisfying the CRC check is obtained, each of which is then encoded to an LDPC codeword. The most likely codeword among them is the output of the decoding approach. The simulation results indicate that the proposed two-stage decoding approach can outperform the traditional BP-based iterative algorithm with a large maximum number of iterations. Moreover, the average complexity of the proposed approach is relatively low.
In this paper, we improve performance of Low Density Parity Check (LDPC) codes by adding a large number of short cycles. Short cycles, especially cycles of length 4, degrade performance of LDPC codes if the standard BP (Belief Propagation) decoding is used. Therefore current researches have focused on removing cycles of length 4 for designing good performance LDPC codes. We found that a large number of cycles of length 4 improve performance of LDPC codes if a modified BP decoding is used. We present the modified BP decoding algorithm for LDPC codes with a large number of short cycles. We show that the modified BP decoding performance of LDPC codes with a large number of short cycles is better than the standard BP decoding performance of LDPC codes designed by avoiding short cycles.
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.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.