This letter introduces a combinatorial construction of girth-eight high-rate low-density parity-check codes based on integer lattices. The parity-check matrix of a code is defined as a point-line incidence matrix of a 1-configuration based on a rectangular integer lattice, and the girth-eight property is achieved by a judicious selection of sets of parallel lines included in a configuration. A class of codes with a wide range of lengths and column weights is obtained. The resulting matrix of parity checks is an array of circulant matrices.

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In this paper we propose a novel approach to modulation and error control coding. The idea is to completely eliminate a constrained code and, instead, impose the constraint by the deliberate introduction of bit errors before transmission. The redundancy that would have been used for imposing the constraint is used in our scheme to strengthen the error control code (ECC), in such a way that the ECC becomes capable of correcting both deliberate errors as well as channel errors that occurs during the detection. The proposed ECC-modulation scheme is based on iterative decoding of low-density parity-check codes (LDPC) and a runlength constraint.