Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Approximation algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating-CVP to within Almost-Polynomial Factors is NP-Hard
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Hardness of approximating the minimum distance of a linear code
IEEE Transactions on Information Theory
On decoding of low-density parity-check codes over the binary erasure channel
IEEE Transactions on Information Theory
Stopping set distribution of LDPC code ensembles
IEEE Transactions on Information Theory
On the stopping distance and the stopping redundancy of codes
IEEE Transactions on Information Theory
Improved Upper Bounds on Stopping Redundancy
IEEE Transactions on Information Theory
An efficient algorithm to find all small-size stopping sets of low-density parity-check matrices
IEEE Transactions on Information Theory
On the hardness of approximating stopping and trapping sets
IEEE Transactions on Information Theory
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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 ε 0 unless NP⊆DTIME(npoly(logn)).