Quasi-Cyclic Spatially Coupled LDPC Codes Construction with Girth Eight

Small cycles in spatially coupled low-density paritycheck (SC-LDPC) codes have a detrimental effect on the error floor. Recently, an explicit simple method has been proposed to construct a class of 4-cycle free SC-LDPC codes by partitioning a spreading matrix into a number of component matrices. Using a quasi-cyclic (QC) lifting, we propose a component matrices construction method to obtain QC-SC-LDPC codes with a girth eight in this paper. The component matrices of the new method are completely defined by a spreading matrix and an exponent matrix. The spreading matrix is constructed from a finite sequence of integers, and the exponent matrix is constructed from the greatest common divisor (GCD) framework. The novel construction method demonstrates the capacity to entirely eliminate 6-cycles. Compared to the recently proposed explicit structural design, the proposed code achieves a girth of eight and exhibits better bit-error rate (BER) performance.