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Determination of the shortest balanced cycles in QC-LDPC codes Matrix

Xiao Rong Gao, Nan Zhang

Published Jan 1, 2011• 1 citation
OpenAlex

Abstract

In this paper, we determinate the shortest balanced cycles of quasi-cyclic low-density parity-check (QC-LDPC) codes. We show the structure of balanced cycles and their necessary and sufficient existence conditions. Furthermore, we determine the shortest matrices of balanced cycle. Finally all nonequivalent minimal matrices of the shortest balanced cycles are presented in this paper.

Related papers

Analysis of balanced cycles of QC-LDPC codes

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IFIP International Conference on Wireless and Optical Communications Networks (WOCN)•May 1, 2011•2 citations

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An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.

arXiv:1705.10717•May 30, 2017•0 citations
In this paper, we determinate the shortest balanced
cycles of quasi-cyclic low-density parity-check (QC-LDPC) codes.
We show the structure of balanced cycles and their necessary and
sufficient existence conditions. Furthermore, we determine the
shortest matrices of balanced cycle. Finally all nonequivalent
minimal matrices of the shortest balanced cycles are presented in
this paper.
In this paper, we investigate the cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation of a parity-check matrix for a QC-LDPC code, we analyze a necessary and sufficient condition for a cycle of a given length to exist. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. We also give a bound which is a sufficient condition for a QC-LDPC code of a given girth to be constructed by a greedy algorithm. The bounds derived here are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds in many classes of regular LDPC codes.
In this paper we investigate the cycle properties of regular quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation, we analyze the conditions for short cycles to exist in regular QC-LDPC codes and then give necessary conditions for avoiding short cycles in terms of their parameters. Numerical results show that our bounds on the number of rows in the parity-check matrices for regular QC-LDPC codes without cycles of length 4 or 6 are tighter than any other known bounds.
Short cycles in the Tanner graph of a low-density parity-check (LDPC) code may cause a severe performance degradation. In this paper, we investigate the cycle properties of quasi-cyclic LDPC (QC-LDPC) codes. We first analyze a necessary and sufficient condition for a cycle of a given length to exist, by using the sequence representation of a parity-check matrix for a QC-LDPC code. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. Our necessary conditions are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds for many classes of regular QC-LDPC codes.
An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.