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IEEE International Conference on Communication Systems (ICCS)

A method to construct girth-8 low density lattice codes

Xiaosong Wang, Guiran Chang

Published Nov 1, 2008• 2 citations
Publisher

Abstract

First a new lattice coding scheme, low density lattice codes (LDLC), and its iterative decoding algorithm are introduced in this paper. Based on circular shift of the candidate sequence and the removal of size-6 loop, a new method is proposed to form a LDLC check matrix with minimum loop size 8. Simulation results show that the performance using the girth-8 check matrix can be improved efficiently.

DOI
10.1109/iccs.2008.4737184

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First a new lattice coding scheme, low density lattice codes (LDLC), and its iterative decoding algorithm are introduced in this paper. Based on circular shift of the candidate sequence and the removal of size-6 loop, a new method is proposed to form a LDLC check matrix with minimum loop size 8. Simulation results show that the performance using the girth-8 check matrix can be improved efficiently.
In order to find a kind of linear code with simple structure and approaching Shannon limit,based on the algorithm of constructing quasi-cyclic low density parity check(LDPC) codes and combined with the characteristic of low density lattice codes(LDLC),the LDLC with girth-8 through improving the algorithm was constructed.The new algorithm ensures the LDLC generating sequence distribute in each row or each column randomly and its uniformity in each row and each column.Meanwhile this article analyses the complexity of the algorithm.Simulation result in AWGN channel shows that the performance of girth-8 LDLC code using the proposed algorithm is better than the present girth-6 LDLC code.
In order to decode efficiently,a LDLC( Low Density Lattice Codes) check matrix without short loops needs to be constructed. In this paper, a method based on subset-matrix is applied that all 4-loops and 6-loops are removed in subset-matrix,and after combining with Tanner graph,the needed LDLC check matrix can be got. By using subset-matrix,computation complexity has nothing to do with the code length and no new short loop is generated,and the LDLC codes with variable code length can be constructed by using this method. Simulation result in AWGN channel shows that,by applying this method removing all 6-loops,the performance in decoding is much better compared with the LDLC code with no 4-loop.
Enabling the parity-check matrices to have a large girth is an efficient method to improve the decoding performance for many binary and non-binary QC-LDPC codes.A new explicit framework to construct QC-LDPC codes with girth at least eight is proposed,without any computer search procedures.The QC-LDPC codes constructed by the framework not only have a girth at least eight,but also possess an advantage of consecutive cyclic permutation matrix(CPM) sizes.The framework includes two steps:first,a parity-check matrix is explicitly constructed with a girth at least eight under an infinite CPM size;second,the tight lower bound of consecutive CPM sizes is precisely calculated directly from the corresponding shift matrix of the parity-check matrix,by employing a new girth property discovered by this paper.
A novel and simple construction of regular LDPC codes was proposed, which used sparse binary sequences, through studying construction methods of LDPC codes. The distribution matrix of ones in parity-check matrix was introduced into the new construction. The cyclic cross correlation function and the cyclic auto correlation function were utilized to ensure that the girth of Tanner graph was eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the LDPC codes.