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International Journal of Advancements in Computing Technology

A New Nonbinary Quasi-cyclic LDPC Codes Construction Algorithm

Tong Ningning -, WU Yu-ping

Published Apr 30, 2013• 3 citations
Publisher

Abstract

An algorithm for constructing nonbinary Quasi-cyclic LDPC (QC-LDPC) codes on the basis of masking and puncturing techniques in consideration of the shortage of algebraic construction algorithm and time-varying performance of wireless channels is proposed . This scheme can reduce the complexity of the hardware implementation, enhance the error correction performance of the LDPC codes constructed by structure algorithm based on masking technology, and improve the average effectiveness of the communication system by realizing a rate-compatible encoding based on puncturing technology. The simulation results show that the nonbinary LDPC codes constructed with masking and puncturing techniques can provide significantly stronger error correction capabilities as compared with those constructed with algebraic method which are used directly.

DOI
10.4156/ijact.vol5.issue8.142

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An algorithm for constructing nonbinary Quasi-cyclic LDPC (QC-LDPC) codes on the basis of masking and puncturing techniques in consideration of the shortage of algebraic construction algorithm and time-varying performance of wireless channels is proposed . This scheme can reduce the complexity of the hardware implementation, enhance the error correction performance of the LDPC codes constructed by structure algorithm based on masking technology, and improve the average effectiveness of the communication system by realizing a rate-compatible encoding based on puncturing technology. The simulation results show that the nonbinary LDPC codes constructed with masking and puncturing techniques can provide significantly stronger error correction capabilities as compared with those constructed with algebraic method which are used directly.
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.
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.
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.
This paper presents two simple and very flexible methods for constructing non-binary (NB) quasi-cyclic (QC) LDPC codes. The proposed construction methods have several known ingredients including base array, masking, binary to nonbinary replacement, and matrix-dispersion. By proper choice and combination of these ingredients, NB-QC-LDPC codes with excellent performance can be constructed. The constructed codes can be decoded with a reduced-complexity iterative decoding scheme which significantly reduces the hardware implementation complexity.
Due to quasi-cyclic structure of parity-check matrices, Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes reduce hardware requirements, and thus they have a higher practical value than random LDPC codes. This paper proposes an improved construction method of QC-LDPC based on PEG Algorithm, and the girth of the QC-LDPC codes has an increase of 2. Firstly, a base matrix is generated by the PEG algorithm, and then the base matrix is expanded using the unit circle permutation matrix, at the same time, the short loop of the base matrix is eliminated. This approach has the advantages of the PEG algorithm and the QC-LDPC codes, and simulation results show that bit error rate (BER) performance of the QC-LDPC codes presented in this paper is the same as or exceeds the one of randomly constructed LDPC codes.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.