|| Construction of Algebraic-Based Variable-Rate QC-LDPC Codes
||Huaan Li, Baoming Bai, Xidian University, China; Hengzhou Xu, Zhoukou Normal University, China; Chao Chen, Xidian University, China|
||D1-S6-T2: Quasi-Cyclic LDPC Codes
||Monday, 12 July, 23:40 - 00:00
||Tuesday, 13 July, 00:00 - 00:20
In this paper, we concentrate on one algebraic-based quasi-cyclic low-density parity-check (QC-LDPC) code constructed from two subsets of a finite field and generalize it to propose a class of variable-rate QC-LDPC (VR-QC-LDPC) codes, whose parity-check matrices are nested horizontally and have constant number of rows. Thus the proposed codes are significant at least in terms of storage complexity and can be simply implemented. The constructed codes also inherit the original algebraic-based QC-LDPC codes and their exponent matrices can be obtained from two subsets of the given finite field. We hereby analyze the structural properties from the isomorphism perspective, and present some rules to significantly prune the size of search space and determine the non-isomorphic exponent matrices. By distinguishing the smaller quantities of non-isomorphic matrices with cycle property metric, we can easily construct a series of nested exponent matrices with better cycle distributions and obtain the VR-QC-LDPC codes. Numerical results demonstrate that the constructed codes have better iterative decoding performance within a range of code rates and decoding iterations.