Study of low-density parity-check decoding algorithms

Pao Yue-kong Library Electronic Theses Database

Study of low-density parity-check decoding algorithms

 

Author: Jia, Ru
Title: Study of low-density parity-check decoding algorithms
Degree: M.Sc.
Year: 2012
Subject: Error-correcting codes (Information theory)
Coding theory -- Mathematics.
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Electronic and Information Engineering
Pages: x, 94 leaves : ill. ; 30 cm.
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2522629
URI: http://theses.lib.polyu.edu.hk/handle/200/6623
Abstract: Low-density parity-check (LDPC) code is a class of error-correcting codes whose capacity approaches Shannon's limit. Due to the advantages of LDPC codes, such as lower decoding complexity and lower the error floor, its applications on reliable communications attract academic field and IT industrial field's high attention. Nowadays, it becomes one of the most attractive topics in channel coding. In this thesis, on the basis of existing theory of LDPC codes, the LDPC decoding ideas are analyzed and summarized systemically. The detailed derivation of the sum-product algorithm about information updated principles based on both additive white Gaussian noise (AWGN) channels and log-likelihood ratio is shown. With the algorithm mentioned above, an estimated and approximate algorithm (min-sum decoding algorithm) is given. Moreover, modifications to the min-sum decoding algorithm are proposed. Modified min-sum decoding algorithm can improve the performance while the complexity of the algorithm is increasing. To reduce the computation complexity, quantization and clipping methods on sum-product and min-sum decoding algorithms with a little performance loss are introduced. In many cases, 4-bit quantized decoding algorithms are close to ideal performance in a wide range of signal-to-noise ratio. In this thesis, a lot of simulations on sum-product decoding algorithm, min-sum decoding algorithm, quantized sum-product decoding algorithm, quantized min-sum decoding algorithm and modified min-sum decoding algorithm are performed. Through analyzing the simulation results, the basis of existing theory of LDPC codes is validated. The performance of quantized decoding algorithm with different number of levels is compared. Comparing the modified min-sum decoding algorithm with the original algorithm (no modification and quantization), the advantage and characteristic of the modified min-sum decoding algorithm are illustrated. Future work can include improving the encoding and decoding algorithms of LDPC codes, and construction of LDPC codes.

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