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Journal of Wireless Networking and Communications

Reduced Complexity of Decoding Algorithm for Irregular LDPC Codes Using a Split Row Method

Rachid El Alami, Mostafa Mrabti, Cheikh Bamba Gueye

Published Aug 31, 2012• 5 citations
Publisher

Abstract

In this paper, we have proposed a novel method of decoding algorithm of irregular LDPC codes. A reduced complexity LDPC decoding method for regular LDPC code is extended to irregular LDPC codes. We present in this paper a full description of this method and its benefits for various row weight and length code word. The Split-Row method makes column processing parallelism easier to exploit and significantly simplifies row processors. Recently, irregular LDPC codes have received a lot of attention by many advanced standard, such as WiFi, WiMAX Mobile and digital video broadcasting (DVB-S2). Hence the idea to develop the “Split-Row Method” for irregular LDPC codes. In this context, we have performed an implementation on MATLAB of an irregular LDPC codes with different code word and code rate; simulation results over an additive white Gaussian channel show that the error performance of high row-weight codes with Split-Row decoding is within 0.3–0.5 dB of the Min-Sum algorithm. The study result shows that the “Split Row Method” is better for irregular code than regular LDPC codes.

DOI
10.5923/j.jwnc.20120204.01

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In this paper, we have proposed a novel method of decoding algorithm of irregular LDPC codes. A reduced complexity LDPC decoding method for regular LDPC code is extended to irregular LDPC codes. We present in this paper a full description of this method and its benefits for various row weight and length code word. The Split-Row method makes column processing parallelism easier to exploit and significantly simplifies row processors. Recently, irregular LDPC codes have received a lot of attention by many advanced standard, such as WiFi, WiMAX Mobile and digital video broadcasting (DVB-S2). Hence the idea to develop the “Split-Row Method” for irregular LDPC codes. In this context, we have performed an implementation on MATLAB of an irregular LDPC codes with different code word and code rate; simulation results over an additive white Gaussian channel show that the error performance of high row-weight codes with Split-Row decoding is within 0.3–0.5 dB of the Min-Sum algorithm. The study result shows that the “Split Row Method” is better for irregular code than regular LDPC codes.
A reduced complexity LDPC decoding method for regular LDPC code is extended to irregular LDPC codes; we present in this paper a full description of this method and its benefits for various row weight and length code word. The Split-Row method makes column processing parallelism easier to exploit and significantly simplifies row processors. Simulation results over an additive white Gaussian channel show that the error performance of high row-weight codes with Split-Row decoding is within 0.3-0.5 dB of the Min-Sum algorithm.
In this paper, we propose a thresholding algorithm to improve Split-Row decoding method of irregular LDPC codes, with maintaining the same level of complexity. We present in this paper a full description of this method and its benefits for various row weight and length code word. In this context, we have performed an implementation on MATLAB of an irregular LDPC codes with different code word and code rate. Simulation results over an additive white Gaussian channel show that the error performance of high row-weight codes with thresholding algorithm is within 0.1–0.2 dB of the normalized Min-Sum algorithm. The study result shows that the thresholding algorithm outperforms original Split Row of irregular codes.
Recently, LDPC codes have been proved to be capable of closely approaching the channel capacity and hence they are strongly promoted in many international standards. Though decoding is simpler compared to Turbo code decoding, efficient decoding techniques for LDPC codes are in demand to make it further simpler. The theoretical performance of LDPC codes appears simple and close to Shannon’s capacity of channel, but the practical implementation is still challenging due to tasks like numerical inaccuracy, limited memory resources, etc. We investigate methods to reduce the complexity and make decoding simple while still keeping the loss in performance negligible. The aim of this paper is to reduce the complexity by simplification of the component decoders. For this, we analyze the min-sum algorithm and derive a theoretical framework. With this framework, we are able to modify the algorithm in order to achieve good performance for regular as well as irregular LDPC codes.
In this paper, we propose an approach to construct a class of irregular low-density parity-check (LDPC) codes based on row partition.We divide the rows of LDPC check matrix into subsets and derive an approach to arrange '1' in each column to prevent low weight code words.When decoded by iterative algorithm, the proposed codes show performance with low error floor and are subject to few undetected errors.The LDPC codes constructed based on the proposed scheme have efficiently encoding structures.
This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.