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Transactions on Emerging Telecommunications Technologies

Low‐complexity high‐rate irregular QC‐LDPC codes with applications to PR2 and EPR2 channels

Virasit Imtawil, Mongkol Kupimai, A. Kruesubthaworn, Apirat Siritaratiwat, Anupap Meesomboon

Published Nov 23, 2012• 0 citations
Publisher

Abstract

ABSTRACT In this paper, we propose a modified high rate (3,L) quasi‐cyclic low‐density parity‐check (QC‐LDPC) code based on circulant permutation matrices for efficient encoder implementation. The structure of the code is modified from a (3,L) regular QC‐LDPC code to be an approximate lower triangular matrix and a linear independent form. We present two novel efficient encoding techniques for generating redundant parity bits. The complexity of the encoder implementation depends on the number of redundant parity bits of the code for one‐stage encoding and the length of the code for two‐stage encoding. The advantage of both encoding techniques is that few XOR gates are used in encoder implementation. The simulation results show that the proposed codes at code rate 0.884 and 0.953 have good bit error rate performance compared with other LDPC codes over PR2 and EPR2 channels. European Transactions on Telecommunications. Copyright © 2012 John Wiley & Sons, Ltd.

DOI
10.1002/ett.2578

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High-speed, high-reliability requirements and strict power limitation of near-earth communications yield that the channel coding must have high coding gain and lower error floor. In this paper, an irregular quasi-cyclic low-density parity- check (QC-LDPC) code for specific use in near-earth communications is proposed. In order to eliminate the impact of short-cycles and further improve the performance of codes, a base matrix with girth at least 8 is employed. Then dual- diagonal structure is adopted in parity check matrix to reduce encoding complexity. Besides, circulant permutation matrices and zero matrices with different sizes are used to fill the nonzero positions and zero positions of the base matrix so as to remove the complexity of the selection of cyclic shift coefficients. The adoption of circulant permutation matrices with different sizes ensures that the parity check matrix is full rank, which makes the code rate controllable. Finally, simulation results are given to demonstrate the performance of the constructed codes by comparing with several existing codes. Index Terms—Low-density parity-check codes, parity check matrix, circulant permutation matrix, near-earth communications

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International Conference on Advanced Communication Technology•Jan 1, 2017•3 citations
ABSTRACT In this paper, we propose a modified high rate (3,L) quasi‐cyclic low‐density parity‐check (QC‐LDPC) code based on circulant permutation matrices for efficient encoder implementation. The structure of the code is modified from a (3,L) regular QC‐LDPC code to be an approximate lower triangular matrix and a linear independent form. We present two novel efficient encoding techniques for generating redundant parity bits. The complexity of the encoder implementation depends on the number of redundant parity bits of the code for one‐stage encoding and the length of the code for two‐stage encoding. The advantage of both encoding techniques is that few XOR gates are used in encoder implementation. The simulation results show that the proposed codes at code rate 0.884 and 0.953 have good bit error rate performance compared with other LDPC codes over PR2 and EPR2 channels. European Transactions on Telecommunications. Copyright © 2012 John Wiley & Sons, Ltd.
In this paper, the new structure of high rate non-binary QC-LDPC codes based on the circulant permutation matrices is proposed. The construction of parity-check matrix of the proposed codes is obtained from (2, L) regular QC-LDPC codes. The parity-check matrix of the proposed codes has girth greater than 8. Simulation results over PR channels with the high order Galois Field show that the bit error rate and the symbol error rate performance of the proposed codes is better than those of the random non-binary LDPC codes, both in PR2 channel and EPR2 channel.
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
Quasi Cyclic Low Density Parity Check codes (QC-LDPC) is proposed to reduce the complexity of the Low Density Parity Check codes (LDPC) further while obtaining the similar performance. Our proposed QC-LDPC presents an improved construction of circulant sub-matrices based QC-LDPC at high SNR. The proposed construction yields a performance gain of about 1 dB at a 0.0003 bit error rate (BER). Proposed code is tested on 4 types of decoding algorithm and compared. Proposed algorithm is also compared with the existing QC-LDPC and the proposed approach outperforms the existing one at high SNR. Simulation is also performed varying the number of horizontal submatrix and the result shows that the parity check matrix with smaller horizontal concatenation shows better performance.
SUMMARY Low encoding complexity is very important for quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC‐LDPC codes with low encoding complexity. This scheme is called two‐stage particle swarm optimization (TS‐PSO) algorithm, in which both the threshold and girth distribution of QC‐LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC‐LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC‐LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity‐check matrix of the QC‐LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC‐LDPC codes constructed by proposed scheme, the QC‐LDPC code in 802.16e standard, and the QC‐LDPC code in Tam's study. Simulation results show that the QC‐LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC‐LDPC codes with low encoding complexity. Copyright © 2012 John Wiley & Sons, Ltd.
High-speed, high-reliability requirements and strict power limitation of near-earth communications yield that the channel coding must have high coding gain and lower error floor. In this paper, an irregular quasi-cyclic low-density parity- check (QC-LDPC) code for specific use in near-earth communications is proposed. In order to eliminate the impact of short-cycles and further improve the performance of codes, a base matrix with girth at least 8 is employed. Then dual- diagonal structure is adopted in parity check matrix to reduce encoding complexity. Besides, circulant permutation matrices and zero matrices with different sizes are used to fill the nonzero positions and zero positions of the base matrix so as to remove the complexity of the selection of cyclic shift coefficients. The adoption of circulant permutation matrices with different sizes ensures that the parity check matrix is full rank, which makes the code rate controllable. Finally, simulation results are given to demonstrate the performance of the constructed codes by comparing with several existing codes. Index Terms—Low-density parity-check codes, parity check matrix, circulant permutation matrix, near-earth communications
Cyclically-coupled quasi-cyclic low-density parity-check (CC-QC-LDPC) codes are a new class of QC-LDPC codes which can achieve excellent error performance and relatively low hardware requirement. In this paper, we modify the CC-QC-LDPC code construction by using random permutation matrices instead of circulant permutation matrices, forming the “random-permutation-matrix-based CC-LDPC (RP-CC-LDPC) code”. The objective is to achieve a better error performance under the same code length. We simulate the bit error rate using FPGA simulations. We also compare the BER results and decoder complexity of the above codes with those of regular and irregular QC-LDPC codes under the same code length and code rate.