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IET International Conference on Wireless, Mobile and Multimedia Networks (ICWMMN)

Construction of nonbinary LDPC codes: prime difference approach

Xin Zhao, Lijun Zhang, L. L. Cheng

Published Jan 1, 2011• 0 citations
Publisher

Abstract

This paper presents an algebraic method for constructing structural nonbinary LDPC codes based on the prime difference over finite field. The approach gives a class of quasi-cyclic (QC)-LDPC codes with girth at least 6. Especially, the approach can construct a class of short length code and the decoding complexity is low. Simulation results show that the constructed codes decoded with iterative decoding perform well over the AWGN channel using BPSK transmission in terms of bit-error probability and rate of decoding convergence, collectively.

DOI
10.1049/cp.2011.0970

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This paper presents an algebraic method for constructing structural nonbinary LDPC codes based on the prime difference over finite field. The approach gives a class of quasi-cyclic (QC)-LDPC codes with girth at least 6. Especially, the approach can construct a class of short length code and the decoding complexity is low. Simulation results show that the constructed codes decoded with iterative decoding perform well over the AWGN channel using BPSK transmission in terms of bit-error probability and rate of decoding convergence, collectively.
In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4,ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.
In the late 1950's and early 1960's, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for correcting random errors with algebraic decoding, such as Bose-Chaudhuri-Hocqenghem (BCH) and Reed-Solomon (RS) codes. Recently it has been shown that finite fields can also be used successfully to construct binary quasi-cyclic (QC)-LDPC codes that perform very well not only over the AWGN channel but also over the binary erasure channel with iterative decoding, besides being efficiently encodable. This paper is concerned with constructions of nonbinary QC-LDPC codes based on finite fields
In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4, p) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin. Keywords-nonbinaryLDPCcodes; finite fields; automorphism; Cycles-LimitedLDPCcodes
In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is based on the multiplicative inverses of nonzero elements in finite fields and gives a class of quasi-cyclic codes with girth 6, the second method gives a class of (3, rho) quasi-cyclic codes with girth 8, the third method gives a class of structured codes with cycles limited. The codes given in examples perform well over AWGN channel and have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Shu Lin.
In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.