对于围长(girth)至少为8的低密度奇偶校验(LDPC)码,目前的绝大多数构造方法都需要借助于计算机搜索。受贪婪构造算法启发,该文利用完全确定的方式构造出一类围长为8的(3,L)-规则QC-LDPC码。这类QC-LDPC码的校验矩阵由3×L个P×P的循环置换矩阵构成。对于任意整数P≥3L^2/4,这类校验矩阵的围长均为8。
Most of the proposed constructions for Low-Density Parity-Check (LDPC) codes with girth at least eight are focused on (semi-) stochastic methods with the aid of computer search. Motivated by the resulting parity-check matrices obtained from the Greedy construction idea, a deterministic method is presented to construct a novel family of girth-8 (3,L)-regular Quasi-Cyclic (QC-) LDPC codes. The parity-check matrix of the new code consists of 3 × LP × Pcyclic permutation matrices and the girth of its Tanner graph is eight for arbitrary integer P ≥ 3L^2/ 4.