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IEEE Symposium on Computers and Communications (ISCC)

Construction of Girth 8 LDPC Codes based on Multidimensional Finite Lattices

John Craddock, Mark F. Flanagan, Stephen James Redmond, Anthony Fagan

Published Jul 1, 2007• 0 citations
Publisher

Abstract

This paper presents a novel method for constructing low density parity check (LDPC) codes with a girth of up to 8. These codes are based on the structural properties of finite lattices. Results are presented which show that these codes perform well over AWGN channels with iterative decoding.
DOI
10.1109/iscc.2007.4381604

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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
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Quasi-cyclic low-density parity-check (QC-LDPC) codes are known to have algebraic structure, which suits hardware implementation. However, low girth makes their performances worse than random structured LDPC codes. Based on independent row-column mapping sequence, this work proposed a generalized method of constructing QC-LDPC codes with girth eight, which enlarges the class of girth eight QC-LDPC codes to a fairly general series. Simulation results show that the bit error rate of the constructed codes is close to that of progressive edge growth (PEG) based QC-LDPC codes under iterative decoding.