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Computer Engineering and Applications Journal

Improved EBF algorithm of LDPC codes

WU Yu-ping

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

EBF algorithm is one of the best known methods for constructing LDPC codes at short and intermediate block lengths,however,the codewords directly designed by such algorithm have high encoding complexity,which hinders the development of LDPC codes in the practical process.The paper presents an improved EBF algorithm based on iterative encoding method with the linear coding complexity,the aim is to make the coding complexity lower through the improvement of coding scheme and the structure of parity-check matrix.The simulation results indicate that,in the condition of BPSK、QPSK and 16QAM modulations,though there are the same error correct performance between the codewords constructed by improved EBF algorithm proposed in this paper and codewords constructed by EBF algorithm,the powerful advantage lies in the lower hardware complexity.

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EBF algorithm is one of the best known methods for constructing LDPC codes at short and intermediate block lengths,however,the codewords directly designed by such algorithm have high encoding complexity,which hinders the development of LDPC codes in the practical process.The paper presents an improved EBF algorithm based on iterative encoding method with the linear coding complexity,the aim is to make the coding complexity lower through the improvement of coding scheme and the structure of parity-check matrix.The simulation results indicate that,in the condition of BPSK、QPSK and 16QAM modulations,though there are the same error correct performance between the codewords constructed by improved EBF algorithm proposed in this paper and codewords constructed by EBF algorithm,the powerful advantage lies in the lower hardware complexity.
Progressive-edge-growth(PEG) algorithm is much effective for constructing LDPC codes with short and intermediate block lengths.However,the complexity of the codes produced by such algorithm is directly proportional to the square of code length,which hinders the development of LDPC code's implementation.To solve such a problem,this paper presents an improved PEG algorithm which can be encoded by the iterative encoding algorithm with linear coding complexity.The simulation results indicated that,for MSK modulation,the obvious advantage of the presented method is its low complexity in hardware implementation although the error-correcting capability of irregular LDPC codes constructed by the proposed methods is basically identical to that of the codes constructed by the PEG algorithm.
Progressive-edge-growth (PEG) algorithm is one of the best known methods for constructing LDPC codes at short and intermediate block lengths, however, the codes directly designed by such algorithm has high encoding complexity, especially for q-ary LDPC codes, encoding complexity increases with the increase of q value rapidly, which hinder the development of q-ary LDPC code’s implementation seriously. To such problem, the paper presents a improved method based on PEG algorithm which can be encoded by the iterative encoding algorithm with the liner operation complexity. The simulation results indicate: Though the error correcting capability of irregular q-ary LDPC codes constructed by the proposed methods in the paper is basically identical with the codes constructed by the PEG algorithm, but the powerful advantage makes it be easily implemented by the hardware .
Due to quasi-cyclic structure of parity-check matrices, Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes reduce hardware requirements, and thus they have a higher practical value than random LDPC codes. This paper proposes an improved construction method of QC-LDPC based on PEG Algorithm, and the girth of the QC-LDPC codes has an increase of 2. Firstly, a base matrix is generated by the PEG algorithm, and then the base matrix is expanded using the unit circle permutation matrix, at the same time, the short loop of the base matrix is eliminated. This approach has the advantages of the PEG algorithm and the QC-LDPC codes, and simulation results show that bit error rate (BER) performance of the QC-LDPC codes presented in this paper is the same as or exceeds the one of randomly constructed LDPC codes.
In order to ensure the reliability, stability and high transmission rate of fifth-generation mobile communication technology(5G), this paper proposes a hybrid check matrix construction algorithm based on iterative coding algorithm with linear coding complexity. Firstly, this paper improves the traditional iterative coding algorithm and makes it suitable for non-binary low density parity check(NB-LDPC) codes. Then it adopts backward iterative method to change the coding scheme and the structure of the check matrix so that the progressive edge growth(PEG) algorithm has a lower triangular structure and uses it as the base matrix. Finally, a QC-LDPC algorithm with a lower triangular structure is used to generate a cyclic shift matrix and a finite field coefficient matrix. At the same time, the effect of the short loop is eliminated, and an optimal check matrix is selected from the algorithm. Simulation results show that the non-binary LDPC code constructed by the hybrid construction algorithm not only has linear coding and storage complexity, but also has strong error correction capability.
The high encoding complexity of LDPC codes can be solved by designing structured parity-check matrix. If the parity-check matrix of LDPC codes is composed of same type of blocks, decoder implementation can be simple, this structure allow structured decoding and required memory for storing the parity-check matrix can be reduced largely. In this paper, we propose a construction algorithm for short block length structured LDPC codes based on girth condition, PEG algorithm and variable node connectivity. The code designed by this algorithm shows similar performance to other codes without structured constraint in low SNR and better performance in high SNR than those by simulation
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.