Circulant Arrays on Cyclic Subgroups of Finite Fields: Rank Analysis and Construction of Quasi-Cyclic LDPC Codes

摘要

This paper consists of three parts. The first part presents a large class ofnew binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whoseparity-check matrices are constructed based on cyclic subgroups of finitefields. Experimental results show that the codes constructed perform well overthe binary-input AWGN channel with iterative decoding using the sum-productalgorithm (SPA). The second part analyzes the ranks of the parity-checkmatrices of codes constructed based on finite fields with characteristic of 2and gives combinatorial expressions for these ranks. The third part identifiesa subclass of constructed QC-LDPC codes that have large minimum distances.Decoding of codes in this subclass with the SPA converges very fast.