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IEEE Access

Optimized Construction of Protograph G-LDPC Codes by Modified EXIT Chart and MACE for New-Generation Wireless Communications

Jianrong Bao, Bin Jiang, Chao Liu

Published Jan 1, 2018• 4 citations
Publisher

Abstract

In this paper, a new systematic construction of optimized protograph generalized low-density parity-check codes with good decoding threshold and low error floor is proposed. First, a typical code graph is generated by combining an accumulate-repeat-accumulate seed protograph with a Tanner graph extension of a simple linear block node. Subsequently, it is analyzed and optimized theoretically, especially with the puncture mechanism, by a modified extrinsic information transfer chart and an asymptotic weight distribution. The generated graph is then extended to a base matrix by a copy-and-permute procedure, accompanied with the matrix split, which is optimized by a progressive edge growth for good randomness and girth property. Finally, the proposed code matrix is created by replacing “1”in the above base matrix with square circulant sub-matrices, the offsets of which are searched by a quasi-cyclic (QC)-oriented modified approximate cycle extrinsic message degree algorithm to improve the cycle relationship, especially for the compound cycles. Simulation results show that the codes exhibit excellent performance in both error floor and waterfall region on an additive white Gaussian noise channel. Moreover, they are also characterized by faster encoding due to the QC structure as well as lower decoding complexity and less latency, which make them a natural fit for new-generation power constrained wireless communications.

DOI
10.1109/access.2018.2873058

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arXiv:1102.0424•IEEE Transactions on Communications•Mar 13, 2012•24 citations
In this paper, a new systematic construction of optimized protograph generalized low-density parity-check codes with good decoding threshold and low error floor is proposed. First, a typical code graph is generated by combining an accumulate-repeat-accumulate seed protograph with a Tanner graph extension of a simple linear block node. Subsequently, it is analyzed and optimized theoretically, especially with the puncture mechanism, by a modified extrinsic information transfer chart and an asymptotic weight distribution. The generated graph is then extended to a base matrix by a copy-and-permute procedure, accompanied with the matrix split, which is optimized by a progressive edge growth for good randomness and girth property. Finally, the proposed code matrix is created by replacing “1”in the above base matrix with square circulant sub-matrices, the offsets of which are searched by a quasi-cyclic (QC)-oriented modified approximate cycle extrinsic message degree algorithm to improve the cycle relationship, especially for the compound cycles. Simulation results show that the codes exhibit excellent performance in both error floor and waterfall region on an additive white Gaussian noise channel. Moreover, they are also characterized by faster encoding due to the QC structure as well as lower decoding complexity and less latency, which make them a natural fit for new-generation power constrained wireless communications.
To obtain efficient channel codes with high power efficiency at moderate signal-to-noise ratios (SNRs), an efficient high-rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is optimally constructed. By 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 QC matrix template is generated with required code rate and length by the extrinsic information transfer (EXIT) chart for better decoding threshold. 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 sub-matrices to obtain larger girth for better error floor performance. Moreover, an asymptotic weight distribution (AWD) is employed to keep a low-code-error floor for the code. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC oriented nested loop approximated cycle extrinsic message degree (QC-NLACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph to cut the error floor. Simulation results show that the codes produced by the proposed method show quite good bit-error-rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency brought by the high code rate, and the low complexity by the short code length. Moreover, a series of different rate-compatible LDPC codes can be generated from the same protograph framework with some variable node extensions, which significantly eases the code design. Therefore, the proposed code construction can be efficiently applied in the optimal construction of high-rate and short-length rate-compatible QC-LDPC codes with a high data rate and rational complexity, which makes the codes extremely suited for use in new-generation power-constrained wireless communications.
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.
We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.
An efficient method of constructing irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes is proposed. In order to find the degree distribution with low convergence threshold, the extrinsic information transfer (EXIT) chart is utilized to optimize the degree distribution of LDPC codes. Then, a modified progressive edge growth (PEG) algorithm is used to get the mask matrix with the optimal degree distribution. Finally, the parity-check matrix of QC LDPC code is constructed based on the mask matrix, and the shift values are optimized to eliminate short cycles. Simulation results show that the constructed irregular QC LDPC codes with optimized degree distribution significantly outperform the regular QC LDPC codes in the additive white Gaussion noise (AWGN) channel.
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.
We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to maximize the components of the approximate cycle extrinsic message degree (ACE) spectrum of the code's Tanner graph in a greedy fashion. As a consequence, the designed code would perform well in the error floor region. Moreover, the proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.