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International Conference on Telecommunications and Signal Processing (TSP)

Simulated Annealing Method for Construction of High-Girth QC-LDPC Codes

Vasiliy S. Usatyuk, Ilya Vorobyev

Published Jul 1, 2018• 22 citations
Publisher

Abstract

We present a simulated annealing method that construct high-girth quasi-cyclic low-density parity check (QC-LDPC) codes. The proposed method is applicable to both regular and irregular protograph codes. The method show improvement in term of minimal circulant size compare with previous described methods: Hill-Climbing and improved PEG. Simulated results are presented to demonstrate performance gain of proposed construction method in error-floor region under base graph 2 (BG2) using 5G eMBB standard length adaption method.

DOI
10.1109/tsp.2018.8441303

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International Symposium on Advances in Electrical, Electronics and Computer Engineering (ISAEECE)•Jan 1, 2016•1 citation
We present a simulated annealing method that construct high-girth quasi-cyclic low-density parity check (QC-LDPC) codes. The proposed method is applicable to both regular and irregular protograph codes. The method show improvement in term of minimal circulant size compare with previous described methods: Hill-Climbing and improved PEG. Simulated results are presented to demonstrate performance gain of proposed construction method in error-floor region under base graph 2 (BG2) using 5G eMBB standard length adaption method.
In this paper, we present an improvement of the PEG algorithm for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes with large girth. We introduce the concept of PEG-undetectable cycles on the computation tree in the PEG algorithm for QC-LDPC codes and give a predictive method to avoid these undetected cycles. The aim is to select only the candidates that ensure the maximization of local girth for a code of girth g ≥ 10 and thus avoid a posteriori verification after the creation of a new edge i.e. keep the predictive philosophy of the PEG algorithm. The proposed method is applicable to both regular and irregular codes and also protograph type-I codes. Simulation results are presented to demonstrate the efficiency of our method in terms of minimum circulant permutation matrix pminand error performance.
Multitype quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of protograph LDPC codes lifted cyclically from protographs with multiple edges, represented by two weight and slope matrices. For a given weight-matrix, an approach is proposed to find the maximum-achievable girthgmax⁡g_{\max }gmax​of the corresponding multitype QC-LDPC codes by some inevitable chains having less complexity than the existing methods. This advantage leads to some new patterns of the weight matrices such that the corresponding codes have some improvements in terms of the maximum-achievable girths or the minimum-distance upper-bounds. In continue, for a given weight-matrix with maximum-achievable girthgmax⁡g_{\max }gmax​, some slope-matrices are constructed by a depth-first search algorithm for which the corresponding multitype QC-LDPC codes with even girthggg,g≤gmax⁡g\le g_{\max }g≤gmax​, have smaller lengths, higher rates, or larger minimum-distances than the state-of-the-art achievements. Simulation results show that the constructed codes have some error-rate advantages than PEG, random-like, CCSDS, and 802.11n/ac IEEE standard LDPC codes.
To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.
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.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes require less hardware resources due to the quasi-cyclic structure of parity-check matrices.In this paper, two improved methods for constructing QC-LDPC codes are proposed.Firstly, in order to make sure the masked LDPC codes have flexible code rate and code length, an improved construction of masking matrix is presented.The proposed regular masking matrix of QC-LDPC codes have the girth at least 6.Then, the irregular codes are constructed by using improved finite field approach and PEG algorithm, which result in large girth and less short cycles.Simulations demonstrate that the proposed QC-LDPC codes have both lower error floor and good waterfall performance.