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International Conference on Wireless Communications, Networking and Mobile Computing

Construction of Large Girth (3,k) LDPC Codes Based on Cuboid

Xiongfei Tao, Liu Weizhong, Zou Xuecheng

Published Sep 1, 2006• 1 citation
Publisher

Abstract

The girth and minimum distance are two important factors of LDPC codes. In this paper we construct a type of LDPC codes with girth 8 based on cuboid. The codes are regular, whose column weight is 3. The minimum distance of the code with exact cuboid structure is only 8 and the distribution of code word weight is not optimal, so we proposed a scheme to improve the codes. The simulation results comparing the bit error rate (BER) performance over AWGN channels with randomly constructed LDPC codes shows that our codes are better than the randomly constructed ones

DOI
10.1109/wicom.2006.129

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The girth and minimum distance are two important factors of LDPC codes. In this paper we construct a type of LDPC codes with girth 8 based on cuboid. The codes are regular, whose column weight is 3. The minimum distance of the code with exact cuboid structure is only 8 and the distribution of code word weight is not optimal, so we proposed a scheme to improve the codes. The simulation results comparing the bit error rate (BER) performance over AWGN channels with randomly constructed LDPC codes shows that our codes are better than the randomly constructed ones
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Four classes of maximum-girth geometrically structured column-weight-two regular quasi-cyclic (QC) low-density parity-check (LDPC) codes are introduced. Two classes of these codes, referred to as Type-I and Type-II codes, are with row-weights 4 and 3, and maximum girths 16 and 24, respectively. The idea behind the construction of these two classes of codes, with rates at least 1/2 and 1/3, is slightly generalized to obtain two classes of variable-high-rate codes, referred to as Type-III1 and Type-III2 codes, with maximum girth 20 and 16, respectively. A low-complexity deterministic algorithm for constructing these four classes of codes is given. The algorithm generates maximum-girth Type-I and Type-II codes with almost arbitrary length eta not less than 216 and 243, respectively. The output of the algorithm substantially improves on some of the previously best known codes constructed using a randomized progressive edge-growth (RPEG) algorithm. For instance, we have rate-0.71 Type-III1 codes of lengths 308 and 728 with girths 10 and 12, respectively, versus the code lengths 385 and 840 obtained by the RPEG algorithm. Simulation results on AWGN channel confirm that, from BER performance perspective, the constructed LDPC codes are superior to the column-weight-two LDPC codes constructed by the previously reported methods. The generator matrix G(D) of the convolutional codes associated with Type-I and Type-II codes is given. The free distance dfreeof such a convolutional code is equal to the minimum distance of the corresponding QC block code.
A new method to get lower bound on the minimum distance of regular LDPC codes is presented in this paper.This method,LDPC code is constructed based on indenpendent tree of each variable node in LDPC code.Compared with the random LDPC codes and PEG codes,the LDPC codes constructed in this method result in greater girth and lower bound on the minimum distance.Using the Matlab to simulate,in the AWGN channel,when the length of the codes is 1 008 and 1 512.Simulation results show that new independent tree-based LDPC codes perform the best as the signal-to-noise ration increases.