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International Conference on Communications

A class of structured LDPC codes with large girth

Jin Lu, José M. F. Moura, Urs Niesen

Published Jan 1, 2004• 4 citations
Publisher

Abstract

A class of structured LDPC codes-turbo-structured LDPC (TS-LDPC) codes-composed of two subtrees connected by an interleaver is introduced in this paper. TS-LDPC codes with good girth properties are easy to design: careful design of the interleaver component prevents short cycles in its Tanner graph. A methodology to design TS-LDPC codes with arbitrary column weight j/spl ges/2 and arbitrary girth is also presented. In addition, a complexity reduced decoding algorithm is described. Simulation results demonstrate the good performance of TS-LDPC codes when compared to random LDPC codes of the similar size and rate.

DOI
10.1109/icc.2004.1312524

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•Jun 1, 2011•1 citation
A class of structured LDPC codes-turbo-structured LDPC (TS-LDPC) codes-composed of two subtrees connected by an interleaver is introduced in this paper. TS-LDPC codes with good girth properties are easy to design: careful design of the interleaver component prevents short cycles in its Tanner graph. A methodology to design TS-LDPC codes with arbitrary column weight j/spl ges/2 and arbitrary girth is also presented. In addition, a complexity reduced decoding algorithm is described. Simulation results demonstrate the good performance of TS-LDPC codes when compared to random LDPC codes of the similar size and rate.
Low density parity check (LDPC) codes have stimulated a lot of interest in recent years due to their capacity approaching performance and availability of fast decoding algorithms. The existing encoding scheme for LDPC code usually incurs too high complexity and should be changed to encoding scheme with low complexity. An elementary turbo structured Tanner graph construction and encoding scheme for a family of regular LDPC codes attaining desired high girth is studied in this paper. The construction provides flexibility in choice of parameters like column weight (j > =2), row weight k and arbitrary girth g. Turbo structured low density parity check ( TS-LDPC) codes are regular LDPC codes with their Tanner graph consists of two trees connected by an interleaver. Linear complexity is attained with few alterations and restrictions of in Tanner graph of turbo structured LDPC codes. Simulation results demonstrates that not only the bit error rate (BER) performance of TSLDPC codes at low signal to noise ratio (SNR) is comparable with error performance of corresponding random LDPC codes, with better error performance at high SNR but linear encoding considerably reduces simulation time.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
Low Density Parity Check (LDPC) codes are specified by the parity check matrix H. Smaller girths in the Tanner graphs of LDPC codes prevent the sum-product algorithm from converging, i.e., short cycles in H-matrix degrade the performance of LDPC decoder. In this paper, we present an algorithm for constructing LDPC codes without short cycles. The H-matrix must be sufficiently sparse to increase the girth of a code. In this work, we present a simple method to increase the sparsity of matrix and provide lemmas to avoid short cycles of lengths 4 and 6. We design sub-matrices for column-weight two and column-weight three codes. This design makes use of a simple shifting function given by the proposed scheme. These are then combined into a final H-matrix using Gray code representations. The proposed method provides structured, regular codes with flexibility in code rates and code lengths. The regularity of these codes gives the advantages like simplicity of hardware implementation and fast encoding. Key words LDPC codes, Tanner Graph, Girth, Gray codes
In this paper, we construct regular and irregular LDPC codes using (n, {k1,k2}, 1)block design. The problem of designing regular and irregular structured LDPC codes that have good overall error performance for wide range of code rates and block sizes with attractive storage requirements is attempted. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Further we analyze the constructed codes based on number of short cycles of the corresponding Tanner graph. The analysis shows that codes having small number of short cycles and a cycle structure which is not overly regular in their Tanner graph perform better. The presented codes are well structured and unlike random codes can lend themselves to a very low-complexity encoder and decoder implementation.
An LDPC code construction technique is proposed based on the structural properties of finite m-dimensional lattices. The Tanner graph of any code from this class is shown to have a girth of eight, and the number of proper eightcycles in the graph is enumerated. The minimum distance of the codes is shown to be lower bounded by 2 m. The codes are also shown to be highly flexible in terms of code length and rate, and compatible with a low-complexity serial-parallel decoder implementation based on the turbo-decoding message passing algorithm. Finally, simulation results over the AWGN channel demonstrate that these codes have good error-correcting performance. 1