4-Cycle Free LDPC Codes Based on Difference Sets
Morteza Esmaeili, M. Javedankherad · IEEE Transactions on Communications · 2012
Difference sets are used to give a novel method for constructing structured regular quasi-cyclic low-density parity-check codes. Let Fqbe a field with q elements and assume that D={d1,..., dk} is a (v,k,1)-difference set for Zvwith d12k. Depending on v=q-1, v≥ 2dkor v≥ 2dk-1, three code construction methods are given that produce regular 4-cycle free codes, that is codes with girth at least 6. Simulation results show that the constructed codes perform well over the AWGN channel with an iterative sum-product message-passing decoding algorithm.