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WASE International Conference on Information Engineering

Research on Regular LDPC Codes with better Performance than Turbo Codes

Jian-Bing Han, He Yun He

Published Jul 1, 2009• 4 citations
Publisher

Abstract

A kind of regular LDPC codes is introduced. Its error correct ability is better than Turbo codes' and near to Shannon limit (1.2 dB). The construct of the sparse parity matrix is important. This effects the LDPC codes' error correct ability. In this paper, diagonal method is adopted to construct sparse check matrix of (n,3,6) in approximate lower triangular form by it. This meets the numbers of nonzero elements and randomness. The Belief Propagation algorithm is used in decoding simulation, to this, vector method is proposed which reduces operation time.

DOI
10.1109/icie.2009.280

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A kind of regular LDPC codes is introduced. Its error correct ability is better than Turbo codes' and near to Shannon limit (1.2 dB). The construct of the sparse parity matrix is important. This effects the LDPC codes' error correct ability. In this paper, diagonal method is adopted to construct sparse check matrix of (n,3,6) in approximate lower triangular form by it. This meets the numbers of nonzero elements and randomness. The Belief Propagation algorithm is used in decoding simulation, to this, vector method is proposed which reduces operation time.
A kind of regular LDPC codes is introduced.Its error correcting capability is better than Turbo codes' and approaches to Shannon limit(1.2 dB).The construction of the sparse parity matrix is important,which affects the LDPC codes' error correcting capability.In this paper,the diagonal method is adopted to construct sparse check matrix of(n,3,6) in approximate lower triangle,which meets the numbers of and distribution randomicity of nonzero elements.The belief propagation algorithm is used in decoding simulation,and the vectorization method is proposed to reduce the iteration decoding time.
Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital communications systems, like DVB-S2 and WLAN802.1..This paper aims to know what is LDPC,what its application and introduce encoding algorithms that gives rise to a linear encoding time and also show that the regular and irregular LDPC performance and also introduce different methods for decoding LDPC. I discuss in detail LDPC decoding algorithm: bit flipping algorithm, as a type from hard decision .belief propagation algorithm, sum product algorithm and minimum sum algorithm as examples from soft decision .I expect that at least some students or researchers involved in researching LDPC codes would find this paper helpful.
In this article we present a construction of error correcting codes, that have representation as very sparse matrices and belong to the class of Low Density Parity Check Codes. LDPC codes are in the classical Hamming metric. They are very close to well known Shannon bound. The ability to use graphs for code construction was first discussed by Tanner in 1981 and has been used in a number of very effective implementations. We describe how to construct such codes by using special a family of graphs introduced by Ustimenko and Woldar. Graphs that we used are bipartite, bi-regular, very sparse and do not have short cycles C4. Due to the very low density of such graphs, the obtained codes are fast decodable. We describe how to choose parameters to obtain a desired code rate. We also show results of computer simulations of BER (bit error rate) of the obtained codes in order to compare them with other known LDPC codes.
Low Density Parity Check (LDPC) codes are one of the block coding techniques that can approach the Shannon’s limit within a fraction of a decibel for high block lengths. In many digital communication systems, these codes have strong competitors of turbo codes for error control. LDPC codes performance depends on the excellent design of parity check matrix and many diverse research methods have been used by different study groups to evaluate the performance. Unlike many other classes of codes, LDPC codes are already equipped with a fast, probabilistic decoding algorithm. This makes LDPC codes not only attractive from a theoretical point of view, but also very suitable for practical applications. This paper throws hard decision and soft decision algorithm of LDPC. The hard decision algorithm contains Bit flipping algorithm and Soft decoding algorithm contains Sum product algorithm which is used to correct burst error. Sum Product algorithm is also called as belief propagation. Bit flipping and Sum Product algorithms are explained and can be implemented for the generated parity check matrix of (1016x508) for LDPC code with code rate 1/2.
Low density parity check (LDPC) codes with iterative decoding based on belief propagation (IDBP) achieve astonishing error performance close to the Shannon limit. Until now there has been no known method for constructing these Shannon limit approaching codes systematically. Good LDPC codes are largely generated by computer search. As a result, the encoding of long LDPC codes is in general very complex. This paper presents the first algebraic method for constructing LDPC codes systematically based on finite analytic geometries. Four classes of finite geometry LDPC codes with relatively good minimum distances are constructed. These codes are either cyclic or quasi-cyclic and therefore their encoding can be implemented with simple linear feedback shift registers. Long finite geometry LDPC codes have been constructed and they achieve an error performance only a few tenths of a dB away from the Shannon limit. Finite geometry LDPC codes are strong competitors to turbo codes for error control in communication and digital data storage systems.
Based on the structure of parity-check matrix of RU algorithm,a class of Quasi-cycle Low-density Parity-check(QC-LDPC) codes with complexity is constructed by selecting sub-matrices reasonably to restrict and consisting of lower dual diagonal matrices.Simulation results show that not only the proposed codes have lower complexity,but also the error-correcting performance is better than QC-LDPC codes randomly constructed and practical Block-LDPC codes in the additive white Gaussion noise channel.It can get 0.3 dB Signal to Noise Ratio(SNR) gain at a Bit Error Rate(BRE) of 10-6.