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Journal of Chinese Computer Systems

Designing Linear Encoder for Structured LDPC Codes with Large Girth

Qiongxia Shen

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.In this paper,a novel method based on Column-Difference Search Algorithm and Progressive Edge Growth Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CP-LDPC code has linear encoding complexity.The experimental results show that CP-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.35dB-3.95dB.

Related papers

Design of Structured LDPC Codes with Large Girth

Qiongxia Shen

A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.

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Research on Designing Encoder for a Class of LDPC Codes with Low-Complexity and High-Performance

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In this paper,a novel method based on Column-Difference Search Algorithm and Iterative Filled Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CI-LDPC code has linear encoding complexity.The experimental results show that CI-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.4dB~3.8dB.

Microelectronics & Computer•Jan 1, 2010•0 citations

Construction of LDPC Code with Big Girth and Linear-encoding Complexity

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Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.

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This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.

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Quasi-Cyclic Low-Density Parity-Check Codes Based on Progressive Cycle Growth Algorithm

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Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.

International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)•Jul 1, 2016•1 citation

A Method of Constructing the Half-Rate QC-LDPC Codes with Linear Encoder, Maximum Column Weight Three and Inevitable Girth 26

Li Peng

This paper presents a method of constructing the half-rate irregular quasi-cyclic low-density parity-check codes which can provide linear encoding algorithm and their H-matrices may contain almost the least “1” elements comparing with H-matrices of all existing LDPC codes. This method shows that three kinds of special structural matrices, respectively named as S-matrix, M-matrix and A-matrix, are defined and constructed. With regard to the arbitrary large structural girth based on A-matrix, its general pattern is conceived and its basic rule is proved. A general method of constructing M-matrix with the inevitable girth larger than 24 is introduced by using generalized block design and treating A-matrix as its sub-matrix. S-matrix is generated by substituting specially circular-shift values for non-zero elements in M-matrix. Combining Hd-matrix generated from lifting the S-matrix and Hp-matrix with the approximate lower triangular array structure forms the H-matrix, i.e. H=[Hd Hp], which defines a class of half-rate irregular QC-LDPC codes with maximum column weight 3 and inevitable girth of length 26. Simulation tests show that the performance of the presented QC-LDPC code can achieve the signal-noise-ratio of below 2dB at the bit-error-rate of 10-5, which is comparable with the performance of the practical QC-LDPC codes in industrial Standard, but the complication of the former owing to the least “1” elements in H-matrix is lower than that of the later, as well as the storage requirement is smaller.

Communications•Jan 1, 2014•0 citations
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.In this paper,a novel method based on Column-Difference Search Algorithm and Progressive Edge Growth Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CP-LDPC code has linear encoding complexity.The experimental results show that CP-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.35dB-3.95dB.
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.
In this paper,a novel method based on Column-Difference Search Algorithm and Iterative Filled Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CI-LDPC code has linear encoding complexity.The experimental results show that CI-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.4dB~3.8dB.
Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
This paper presents a method of constructing the half-rate irregular quasi-cyclic low-density parity-check codes which can provide linear encoding algorithm and their H-matrices may contain almost the least “1” elements comparing with H-matrices of all existing LDPC codes. This method shows that three kinds of special structural matrices, respectively named as S-matrix, M-matrix and A-matrix, are defined and constructed. With regard to the arbitrary large structural girth based on A-matrix, its general pattern is conceived and its basic rule is proved. A general method of constructing M-matrix with the inevitable girth larger than 24 is introduced by using generalized block design and treating A-matrix as its sub-matrix. S-matrix is generated by substituting specially circular-shift values for non-zero elements in M-matrix. Combining Hd-matrix generated from lifting the S-matrix and Hp-matrix with the approximate lower triangular array structure forms the H-matrix, i.e. H=[Hd Hp], which defines a class of half-rate irregular QC-LDPC codes with maximum column weight 3 and inevitable girth of length 26. Simulation tests show that the performance of the presented QC-LDPC code can achieve the signal-noise-ratio of below 2dB at the bit-error-rate of 10-5, which is comparable with the performance of the practical QC-LDPC codes in industrial Standard, but the complication of the former owing to the least “1” elements in H-matrix is lower than that of the later, as well as the storage requirement is smaller.