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Hardness of approximation results for the problem of finding the stopping distance in Tanner graphs

Krishnan, Murali K and Chandran, Sunil L (2006) Hardness of approximation results for the problem of finding the stopping distance in Tanner graphs. In: 26th International Conference on Foundations of Software Technology and Theoretical Computer Science,, Dec 13-15, 2006, Calcutta, India, pp. 69-80.

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Abstract

Tanner Graph representation of linear block codes is widely used by iterative decoding algorithms for recovering data transmitted across a noisy communication channel from errors and erasures introduced by the channel. The stopping distance of a Tanner graph T for a binary linear block code C determines the number of erasures correctable using iterative decoding on the Tanner graph T when data is transmitted across a binary erasure channel using the code C. We show that the problem of finding the stopping distance of a Tanner graph is hard to approximate within any positive constant approximation ratio in polynomial time unless P = NP. It is also shown as a consequence that there can be no approximation algorithm for the problem achieving an approximation ratio of 2(log n)(1-epsilon) for any epsilon > 0 unless NP subset of DTIME(n(poly(log n))).

Item Type: Conference Paper
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 01 Sep 2010 05:51
Last Modified: 19 Sep 2010 06:12
URI: http://eprints.iisc.ernet.in/id/eprint/30513

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