33-42

MATRIX ALGORITHM OF THE SIMULATION OF CHANNEL BINARY
AND NONBINARY LDPC CODES

V. A. Fadeev, A. K. Gaisin, A. F. Nadeev
Kazan National Research Technical University named after A. N. Tupolev-KAI,
K. Marx Street, 10, Kazan, 420111, Russian Federation
E-mail: Vladimir_fadeev1993@mail.ru

ABSTRACT

Introduction. Well-known binary low-density parity-check codes (LDPC) are a powerful technique for improving communication system noise immunity owing to their ability of correcting a sufficient number of errors in low signal-to-noise ratios when the number of redundant bits is relatively small. Another advanced approach is a nonbinary extension. Theoretically, it gives greater energy gain and allows realizing sparse structures. It requires smaller blocks of a parity check matrix for coding and decoding. The most important part of the study of LDPC codes is the problems of the efficient use of computing power in the simulation process. Meanwhile simulation algorithms must be maximally optimized for the matrix representation for the efficient use of computer possibilities. The purpose of the work is to design the efficient algorithm of the simulation of binary and nonbinary LDPC codes. Advanced schemes of channel coding and their simulation techniques. The considered coding schemes are very close to the Shannon limit that makes them very promising technologies for the future communication standards such as 5G. A simple coding algorithm is an ideal technique of reducing equipment complexity for upperlink transmission. High noise immunity at a relatively high code speed is one of the reasons for the use of this scheme in channels with severe fading. In order to demonstrate the noise immunity of LDPC codes, the simulation in MatLab environment was carried out using specialized tools - Communication Toolbox. For comparing, Turbo convolutional codes as representatives of the most frequently used in modern telecommunications, were chosen. Results. The mathematical description of procedures of coding and decoding of binary and nonbinary LDPC codes was carried out. In this description, vector, matrix and tensor forms of presentation are used. They allow realizing embedded optimized tools of different simulation environments, such as MatLab, Python. Conclusion. The research showed that noise immunity of binary LDPC codes is higher than noise immunity of turbo codes with less redundancy. Meanwhile, LDPC code decoding complexity is comparable to turbo codes. This kind of channel coding can be equally efficient at correcting single and group errors without interleaving procedures. Results of conducted simulations showed the efficiency of LDPC codes not only for a channel with AWGN, but also for channels with different types of signal fading.

KEYWORDS

binary LDPC codes; nonbinary LDPC codes; channel coding; mobile communication; MatLab; Python.

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For citation: Fadeev V. A., Gaisin A. K., Nadeev A. F. Matrix Algorithm of the Simulation of Channel Binary and Nonbinary LDPC Codes. Vestnik of Volga State University of Technology. Ser.: Radio Engineering and Infocommunication Systems. 2018. No 2 (38). Pp. 33-42. DOI: 10.15350/2306-2819.2018.2.33