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Electronics Optics & Control

A Method for Constructing Quasi-Cycle Extension LDPC Codes with Low Encoding Complexity

Wei Li

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

Progressive-Edge-Growth(PEG) algorithm is an efficient method for constructing LDPC codes with short and intermediate block lengths.However,the complexity of codes produced directly by this algorithm is proportional to quadratic length of the codes,which restricts the implementation of the LDPC codes.To solve the problem,a method was proposed for constructing quasi-cycle extension LDPC codes with low encoding complexity and good error performance.Based on PEG algorithm,a base matrix with an approximate lower triangular was constructed,then all its elements were replaced by circulation permutations.The new method could eliminate the short cycles effectively without changing the degree distribution fraction of the basic matrix.The simulation results show that: compared with LDPC codes generated by PEG algorithm,the LDPC codes presented here have lower encoding complexity and better error performance,which is easy for implementation with hardware.

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Progressive-Edge-Growth(PEG) algorithm is an efficient method for constructing LDPC codes with short and intermediate block lengths.However,the complexity of codes produced directly by this algorithm is proportional to quadratic length of the codes,which restricts the implementation of the LDPC codes.To solve the problem,a method was proposed for constructing quasi-cycle extension LDPC codes with low encoding complexity and good error performance.Based on PEG algorithm,a base matrix with an approximate lower triangular was constructed,then all its elements were replaced by circulation permutations.The new method could eliminate the short cycles effectively without changing the degree distribution fraction of the basic matrix.The simulation results show that: compared with LDPC codes generated by PEG algorithm,the LDPC codes presented here have lower encoding complexity and better error performance,which is easy for implementation with hardware.
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.
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.
The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
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 .
We propose a general method for constructing regular and irregular quasi-cyclic LDPC codes based on the modified PEG (progressive edge growth) graph. The idea of permutation vector is introduced. Through permutation vectors, the QC-LDPC codes based on arbitrary circulant permutation matrices, which are not limited to identity matrix, Q-matrix or D-matrix, can be generated with flexible parameters such as block length, code rate, degree distribution. Simulation results demonstrate that QC-LDPC codes using the new PEG algorithm show an error correction performance comparable to the random LDPC codes based on the traditional PEG algorithm. In addition, the PEG QC-LDPC codes have more hardware-friendly parity check matrices than the random PEG LDPC codes and can fulfill linear-time encoding. The QC-LDPC codes based on D-matrix and Q-matrix are more suitable to be used in QC-LDPC codes than identity matrix because they outperform that of identity matrix by 0.1-0.2 dB in the new PEG algorithm.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.