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IEEE Asia-Pacific Services Computing Conference (APSCC)

Low Complexity Decoding Algorithm of QC-LDPC Code

Fanglong Yi, Pengjun Wang

Published Dec 1, 2010• 3 citations
Publisher

Abstract

Through the research on the decoding algorithm of low-density parity-check (LDPC) code, a low complexity decoding algorithm suitable for quasi-cyclic LDPC (QC-LDPC) code is proposed in this paper. The algorithm adopts layered decoding (LD), and the sub-minimum is replaced by the sum of an optimal correction factor and the minimum during the process of the check nodes update. Therefore, it is not required to find the sub-minimum and the computational complexity reduces significantly. Matlab simulation results show that the decoding performance of this algorithm is very near to min-sum (MS) algorithm, and more superior than single min-sum (SMS) algorithm.

DOI
10.1109/apscc.2010.71

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Through the research on the decoding algorithm of low-density parity-check (LDPC) code, a low complexity decoding algorithm suitable for quasi-cyclic LDPC (QC-LDPC) code is proposed in this paper. The algorithm adopts layered decoding (LD), and the sub-minimum is replaced by the sum of an optimal correction factor and the minimum during the process of the check nodes update. Therefore, it is not required to find the sub-minimum and the computational complexity reduces significantly. Matlab simulation results show that the decoding performance of this algorithm is very near to min-sum (MS) algorithm, and more superior than single min-sum (SMS) algorithm.
Entering the 5G era, the hardware design of low-density parity-check (LDPC) codes under the new standard has increasingly higher requirements on throughput. According to the geometric characteristics of the check matrices of the quasi-cyclicQC) LDCP codes under the CCSDS standard, this paper designs a layered dynamic normalized minimum sum algorithm(LDNMSA) under the pre-termination decoding based on de-layering scheme. The check matrix structure of this code is easy for hardware design and the storage resource consumption is low. The approximate replacement of the minimum sum algorithm(MSA) reduces the computational complexity of the check node update process. The determination of correction factors and inter-layer deletion thresholds through computer simulation improves the decoding performance and the speed of a single iteration, and adopt the layered scheduling scheme with optimized update order reduces the number of iterations required for decoding. Experimental results show that when the bit error rate(BER) is 10-5, the designed algorithm has a gain of approximately 0.5 dB compared to the MSA. The speed and calculation amounts to a single iteration are much lower than the log-likelihood-ratio(LLR) belief propagation(BP) algorithm and the performance is only less than 0.1dB.
Low-density parity-check (LDPC) codes have attracted tremendous attention for their excellent error-correction performance and inherent fitness for high-parallelism implementation. With great complexity reduction and friendly for hardware implementation, the min-sum (MS) decoding algorithm for LDPC codes gains widespread applications in practical. In the MS decoding algorithm, finding the first two minima among input variable-to-check messages is the most complex part. To further reduce the complexity of the MS decoding algorithm, an efficient single-minimum (single-min) based layered MS decoding for quasi-cyclic LDPC (QC-LDPC) codes is proposed in this paper. It is found that statistically the difference between the first minimum and second minimum increases as the decoding becomes more convergent. Accordingly, in the proposed single-min scheme, the second minimum is approximately derived based on the first minimum and an index indicating the convergence degree. Besides, some other metrics that are easily obtained are used to refine the second minimum. Simulation results show that the proposed method can significantly improve the error-correction performance and lower the average number of iterations, compared with the state-of-the-art single-min based MS decoding algorithms.
Quasi Cyclic Low Density Parity Check(QC-LDPC) code is an important branch of LDPC code research.It is a kind of constructed LDPC code with check matrix H constructed by quasi cyclic method.IEEE 802.16e proposes a parity check matrix with quasi cyclic character which makes the encoding and hardware easy to be implemented.This article will mainly introduce the encoding process and analyze the decoding performance of various decoding algorithms.Simulations show that Min-Sum(MS) algorithm compares to the Log-BP performance has approximately 0.5dB loss for high-speed rate coding.And the performance of Normalized Min-Sum(NMS) and Row Weight Matched Min-Sum(Rwm-MS) with relatively low complexity is nearly the same as that of Log-BP algorithm.
Quasi-cyclic low-density parity-check (QC-LDPC) codes are linear block codes with performance close to the Shannon limit. The layered minimum sum (LMS) decoding algorithm speeds up the decoding convergence by layering the check matrix and updating the nodes according to the layers. However, the MS algorithm has the problem of over estimation and affects the decoding performance due to its simplified strategy of MS algorithm updating the message of check nodes. Therefore, this paper proposes a layered minimum sum decoding algorithm based on overestimation. By setting the correction threshold and updating the check nodes by the conditions, the decoding performance is improved. When the code length is 2048 and the bit error rate is , the proposed algorithm can improve the decoding convergence speed by about 25% and obtain a coding gain of about 0.1 dB.
This paper proposes a low-complexity LDPC decoding algorithm with simplified check nodes updating. The proposed algorithm simplifies the result of the second-minimum in check nodes based on the first-minimum computation instead of computing it directly. In order to obtain the approximate result, effective corrected coefficients are utilized, which can reduce the complexity by eliminating the complex computations. Complexity analysis is provided and the results indicate that the complexity of the proposed algorithm is much lower than the general NMS algorithm and MS-based simplified algorithms. Simulation results show that the performance of the proposed algorithm can closely match the NMS algorithm with the same number of iterations.
Next generation wireless systems, such as IEEE802.11n and 802.16e, need high error-correction capacity to achieve high data rate transmission. Therefore, a low-density parity-check code(LDPC code) is adopted as a FEC code. Quasi-cyclic LDPC code(QC-LDPC) code is an important branch of LDPC code research. IEEE 802.16e proposes a parity-check matrix with quasi-cyclic character which makes the encoding very simply. This paper introduces the encoding process and several decoding algorithms for LDPC including Log-BP algorithm, Min-Sum(MS) algorithm and modified MS algorithm. Simulations results under a next generation wireless LAN system show that MS comparing with the Log-BP performance has approximately 0.5dB loss for high-speed rates codes over AWGN channel, however the performance of normalized MS and row weight matched MS with relatively low complexity is nearly the same as that of Log-BP algorithm.