A class of quasi-cyclic LDPC codes from B2(mod m) sequences

Xiao Xiao, Lee

Zhang Guo

A new class of binary low-density parity-check(LDPC)codes is proposed based on B2(mod m) sequences.The parity-check matrix of such a code has a column weight of three and a row weight of an arbitrary integer,and a quasi-cyclic structure.The parity-check matrix also has a girth at least 8,and corresponds to a code with minimal distance at least 12.When m is prime,an 8-cycles reduction method is presented to completely avoid the two types of 8-cycles within the total four types existed in the Tanner graph.Simulation results show that,for a prime integer m,the new LDPC code outperforms the random(quasi-)regular counterpart generated by the PEG algorithm.Finally,a heuristic algorithm based on a strategy called neighboring extension search is presented to search for the B2(mod m)sequences whose lengths approach or meet the upper bound.

GuoHua ZHANG, XinMei WANG

A new class of binary low-density parity-check (LDPC) codes is proposed based on B2(mod m) sequences. The parity-check matrix of such a code has a column weight of three and a row weight of an arbitrary integer, and a quasi-cyclic structure. The parity-check matrix also has a girth at least 8, and corresponds to a code with minimal distance at least 12. When m is prime, an 8-cycles reduction method is presented to completely avoid the two types of 8-cycles within the total four types existed in the Tanner graph. Simulation results show that, for a prime integer m, the new LDPC code outperforms the random (quasi-) regular counterpart generated by the PEG algorithm. Finally, a heuristic algorithm based on a strategy called neighboring extension search is presented to search for the B2(mod m) sequences whose lengths approach or meet the upper bound.

Wenming Liu, Guangxi Zhu, Yongqiang Deng +1 more

Guohua Zhang, Rong Xia Sun, Xinmei Wang

For any row weight L and any circulant permutation matrix size P > ( L − 1) 2 + b 0 ( L − 1) ( b 0 = L − 2 + mod( L ,2)), a class of (3, L ) quasi‐cyclic (QC) low‐density parity‐check (LDPC) codes is explicitly constructed with girth eight, based on the quadratic function f ( x ) = x 2 + bx and its derivative, where b is either of the two integers { b 0 , − b 0 − 2( L − 2)}. Compared with a similar construction from the so‐called difference sequence, the proposed construction is not only much more simple in concept, but also completely deterministic in the sense that no computer search or computing is required. Simulation results show that the new codes significantly outperform the girth‐eight codes constructed by the earliest‐sequence‐based method.

Yuanhua Liu, Meiling Zhang, Jiulun Fan