Combinatorial Designs: Constructions and Analysis
Combinatorial Designs: Constructions and Analysis
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Combinatorial constructions of low-density parity-check codes for iterative decoding
IEEE Transactions on Information Theory
Construction of low-density parity-check codes based on balanced incomplete block designs
IEEE Transactions on Information Theory
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In this paper we propose a method of constructing quasi-cyclic regular LDPC codes from a cyclic difference family, which is a kind of combinatorial design. The resulting codes have no 4-cycle, i.e. cycles of length four and are defined by a small set of generators of codes with high rate and large code length. In particular, for LDPC codes with column weight three, we clarify the conditions on which they have no 6-cycle and their minimum distances are improved. Finally, we show the performance of the proposed codes with high rates and moderate lengths.