Design of Spatially Coupled LDPC Codes with Girth at Least 8

Spatially coupled low-density parity-check (SC-LDPC) codes are a special type of sparse graph codes that have recently attracted great interest due to their capacity-approaching performance. To reduce the performance loss in-curred by short cycles, this paper proposes a method based on the greatest common divisor (GCD) full-length row-multiplier (FLRM) matrix to construct girth-8 quasi-cyclic SC-LDPC codes with improved performance and flexible code rates. Besides, we further extend the lower bound of the circulant permutation matrix (CPM) size to be compatible with different code lengths. Numerical results demonstrate that the proposed SC-LDPC code has performance gains of 1.05 dB and 1.0 dB compared with that based on RS structure at an BER of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup>over AWGN channels for code rates 0.45 and 0.625, respectively. Additionally, SC-LDPC codes based on the GCD constraint achieve the trade-off between decoding performance and complexity..