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Two decision problems related to the computation of stopping sets in Tanner graphs are shown to be NP-complete. It follows as a consequence that there exists no polynomial time algorithm for computing the stopping distance of a Tanner graph unless P=NP.

Two decision problems related to the computation of stopping sets in Tanner graphs are shown to be NP-complete. NP-hardness of the problem of computing the stopping distance of a Tanner graph follows as a consequence.

An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check (LDPC) codes achieving high girth is presented. The construction allows flexibility in the choice of design parameters like rate, average degree, girth and block length of the code and yields an asymptotic family. The complexity of constructing codes in the family grows only quadratically with the block length.

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