Combinatorial constructions of low-density parity-check codes for iterative decoding

Authors:
B. Vasic;O. Milenkovic
Affiliations:
Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ, USA;-
Venue:
IEEE Transactions on Information Theory
Year:
2004

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Abstract

This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.