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Video Engineering

Performance Study on QC-LDPC Code Based on PC-PEG Algorithm Construction

Yang Zhan

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Since LDPC code based on progressive edge growth(PEG) algorithm construction still has many small cycles in the case of maximization of local girth,make use of polynomial cycle(PC) mark to improve PEG algorithm to be enhanced PC-PEG algorithm is proposed in this paper,and it is applied in QC-LDPC.This approach can reduce the number of small circles and improve the performance under the maximization of local girth.By using of QC-LDPC,the parity check matrix is still block based cyclic shift code,this special structure can realize parallel decoding in the engineering and save the storage memory.The experimental results demonstrate that the proposed method has smaller number of girth compared with PEG algorithm,and the special structure of cyclic shift ensures parallel decoding with the same decoding performance.

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Since LDPC code based on progressive edge growth(PEG) algorithm construction still has many small cycles in the case of maximization of local girth,make use of polynomial cycle(PC) mark to improve PEG algorithm to be enhanced PC-PEG algorithm is proposed in this paper,and it is applied in QC-LDPC.This approach can reduce the number of small circles and improve the performance under the maximization of local girth.By using of QC-LDPC,the parity check matrix is still block based cyclic shift code,this special structure can realize parallel decoding in the engineering and save the storage memory.The experimental results demonstrate that the proposed method has smaller number of girth compared with PEG algorithm,and the special structure of cyclic shift ensures parallel decoding with the same decoding performance.
A modified construction method of LDPC (Low-density Parity-check) codes based on polynomial of cycles of PEG (Progressive-Edge-Growth) is proposed according to reaction on the performance of LDPC codes by polynomial of cycles based on PEG and connectivity of cycles. It can reduce the number of the shortest cycles, increase average local girth and improve connectivity of cycles while deleting short cycles by considering girth of check matrix, number of the shortest cycles and ACE (Approximate Cycle EMD), so that it can improve performance of decoding. At the same time, a construction method of QC-LDPC (quasi-cyclic-LDPC) codes based on ACE and polynomial of cycles of PEG is also proposed to deal with the complexity of implementation on hardware of unstructured codes. Simulation results show that the performance of this code is better than unstructured Mackay code and it is easier for implementation on hardware.
In this paper, we propose a method to construct parity-check matrices of Quasi Cyclic (QC) LDPC codes based on the progressive edge-growth (PEG) algorithm with maximized girth property. The proposed algorithm can eliminate short cycles and improve the decoding performance. Simulation results illustrate that the codes constructed with the proposed algorithm have superior performance to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel. At the BER of 10-7, the coding gain of 0.005 dB.
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 a method for constructing Low Density Parity-Check(LDPC) codes based on Tanner graph.Studies show that LDPC codes constructed with the algorithm can achieve excellent error-correcting performance.Based on the algorithm,the Quasi-Cyclic(QC) LDPC codes are proposed in this paper and simulations show that the QC-LDPC codes have almost the same excellent performance as the random codes constructed with the PEG algorithm.In addition,these codes have the property of quasi-cyclic structure,and the encoding and decoding can be implemented with simple shift registers.Besides,the code rates of the LDPC codes constructed with the proposed algorithm are more flexible to be adjusted.
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.