A minimum weight test for a certain subclass of array LDPC codes(HISC2006)

概要

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LDPC codes is a class of linear codes introduced by Gallager in early 60's. Array LDPC (ALDPC) codes is a class of LDPC codes algebraically constructed from a family of array codes. This paper proposes a procedure to check if there is a codeword with specified weight in a certain ALDPC code. The minimum weight of a linear code has strong relationship to the performance of the code, but unfortunately it is difficult to compute the exact minimum weight of long and randomly constructed LDPC codes. We restrict ourselves to a class of complete array LDPC codes (C-ALDPC codes) which is a subclass of array LDPC codes, and investigate positions of nonzero components in a codeword. The code in the considered subclass is invariant under a doubly transitive group of affine permutations. This property gives significant constraint on the positions of nonzero components in a codeword, which means that the positions of nonzero components in a codeword can be classified into rather small number of patterns. Using these conditions, the proposed procedure checks if there exists a codeword with specified weight.
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2006-05-16