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Hybrid of check matrix construction algorithm based on iteration coding algorithm

Jiahui Meng, Zhao Danfeng, Liang Zhang

Published Sep 1, 2018• 0 citations
Publisher

Abstract

In order to ensure the reliability, stability and high transmission rate of fifth-generation mobile communication technology(5G), this paper proposes a hybrid check matrix construction algorithm based on iterative coding algorithm with linear coding complexity. Firstly, this paper improves the traditional iterative coding algorithm and makes it suitable for non-binary low density parity check(NB-LDPC) codes. Then it adopts backward iterative method to change the coding scheme and the structure of the check matrix so that the progressive edge growth(PEG) algorithm has a lower triangular structure and uses it as the base matrix. Finally, a QC-LDPC algorithm with a lower triangular structure is used to generate a cyclic shift matrix and a finite field coefficient matrix. At the same time, the effect of the short loop is eliminated, and an optimal check matrix is selected from the algorithm. Simulation results show that the non-binary LDPC code constructed by the hybrid construction algorithm not only has linear coding and storage complexity, but also has strong error correction capability.

DOI
10.16157/j.issn.0258-7998.181410

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Low-Density Parity-Check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme. Moreover, the nonbinary extension of such codes further increases performance in the short-block regime. In this paper, we review the key elements for the construction of implementation-oriented binary and nonbinary codes. These Quasi-Cyclic LDPC (QC-LDPC) codes additionally feature efficient encoder and decoder implementation frameworks. We then present a versatile algorithm for the construction of both binary and nonbinary QC-LDPC codes that have low encoding complexity and an optimized corresponding graph structure. Our algorithm uses a progressive edge growth algorithm, modified for QC-LDPC graph construction, and then performs an iterative global search for optimized cyclic shift values within the QC-LDPC circulants. Strong error correction performance is achieved by minimizing the number of short cycles, and cycles with low external connectivity, within the code graph. We validate this approach via error rate simulations of a transmission system model featuring an LDPC coder-decoder, digital modulation, and additive white Gaussian noise channels. The obtained numerical results validate the effectiveness of the proposed construction algorithm, with a number of constructed codes exhibiting either similar or superior performance to industry standard binary codes and selected nonbinary codes from the literature.
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In the wireless communication system, it is necessary to change the transmitted code word or code rate in real time according to the channel environment, designing and implementing rate compatible codes is of great practical significance. In allusion to the defects of algebraically constructed QC-LDPC codes algorithm and the time-varying characteristics of wireless channel, we propose an algorithm based on check matrix optimization puncturing technique to construct QC-LDPC codes in this paper. The algorithm selects a high rate matrix with excellent performance as the parent matrix, and then uses the backward node puncturing method to puncture the information bits in the code word from the last column of the check matrix by a multiple of the number of rows to obtain a low rate matrix. The simulation results show that the rate-compatible non-binary LDPC codes constructed by this algorithm not only reduces the complexity of hardware implementation, but also improves the error correction performance of the non-binary LDPC codes, realizes the rate-compatible coding at the same time, and improves the average effectiveness and reliability of the communication system.