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

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2 Author(s)
Vasic, B. ; Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ, USA ; Milenkovic, O.

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.

Published in:

Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 6 )

Date of Publication:

June 2004

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