Computing the Stopping Distance of a Tanner Graph Is NP-Hard

Two decision problems related to the computation f 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.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  Elwyn R. Berlekamp,et al.  On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[3]  Emre Telatar,et al.  Finite-length analysis of low-density parity-check codes on the binary erasure channel , 2002, IEEE Trans. Inf. Theory.

[4]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

[5]  Richard D. Wesel,et al.  Construction of irregular LDPC codes with low error floors , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[6]  Paul H. Siegel,et al.  Improved Upper Bounds on Stopping Redundancy , 2005, IEEE Transactions on Information Theory.

[7]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[8]  Andrea Montanari,et al.  Weight distributions of LDPC code ensembles: combinatorics meets statistical physics , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[9]  J. Kim,et al.  Girth conditioning for construction of short block length irregular LDPC codes , 2004 .

[10]  Alon Orlitsky,et al.  Stopping set distribution of LDPC code ensembles , 2003, IEEE Transactions on Information Theory.

[11]  A. Orlitsky,et al.  Stopping sets and the girth of Tanner graphs , 2002, Proceedings IEEE International Symposium on Information Theory,.

[12]  Alexander Vardy,et al.  The intractability of computing the minimum distance of a code , 1997, IEEE Trans. Inf. Theory.

[13]  Faramarz Fekri,et al.  On decoding of low-density parity-check codes over the binary erasure channel , 2004, IEEE Transactions on Information Theory.

[14]  Alexander Vardy,et al.  On the stopping distance and the stopping redundancy of codes , 2006, IEEE Transactions on Information Theory.