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IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Large-girth LDPC codes based on graphical models

Haotian Zhang, José M. F. Moura

Published Jan 1, 2003• 20 citations
Publisher

Abstract

In this paper we construct two classes of LDPC codes with girth 16 and 20, respectively, based on graphical models. These codes are well-structured, regular, and with column weight j = 2, which greatly simplifies their implementation. The codes with girth g = 16 have code rate r = 1/2. And the codes with girth g = 20 have code rate r = 1/3. Simulation results compare their bit-error-rate (BER) decoding performance in AWGN channels with randomly constructed LDPC codes.

DOI
10.1109/spawc.2003.1318930

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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.
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