On a class of generalized quasi-cyclic codes coming from finite geometries: their systematic encoding and Grobner basis (情報理論)

概要

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Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. It is known that the systematic encoding of GQC codes is equivalent to the division algorithm by Grobner basis of GQC codes. The authors provided an algorithm for the computation of Grobner basis of FG LDPC codes. In this paper, we show that a serial-in serial-out encoder architecture for FG LDPC codes is composed of linear feedback shift registers with the size of the linear order of code-length; to encode a binary codeword of length n, it takes less than 2n adder and 2n memory elements.
社団法人電子情報通信学会の論文
2008-09-04