On the Stopping Distance and Stopping Redundancy of Finite Geometry LDPC Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On the Stopping Distance and Stopping Redundancy of Product Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A cutting-plane method based on redundant rows for improving fractional distance
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Eliminating small stopping sets in irregular low-density parity-check codes
IEEE Communications Letters
The trapping redundancy of linear block codes
IEEE Transactions on Information Theory
Single-exclusion number and the stopping redundancy of MDS codes
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 probabilistic computation of the stopping redundancy of LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Multiple-bases belief-propagation decoding of high-density cyclic codes
IEEE Transactions on Communications
Regular {4,8} LDPC codes and their low error floors
MILCOM'06 Proceedings of the 2006 IEEE conference on Military communications
Hardness of approximation results for the problem of finding the stopping distance in tanner graphs
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Stopping set distributions of algebraic geometry codes from elliptic curves
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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For a linear block code with minimum distance d, its stopping redundancy is the minimum number of check nodes in a Tanner graph representation of the code, such that all nonempty stopping sets have size d or larger. We derive new upper bounds on stopping redundancy for all linear codes in general, and for maximum distance separable (MDS) codes specifically, and show how they improve upon previous results. For MDS codes, the new bounds are found by upper-bounding the stopping redundancy by a combinatorial quantity closely related to Turan numbers. (The Turan number, T(v,k,t), is the smallest number of t-subsets of a v-set, such that every k-subset of the v-set contains at least one of the t-subsets.) Asymptotically, we show that the stopping redundancy of MDS codes with length n and minimum distance d >1 is T(n,d-1,d-2)(1+O(n-1)) for fixed d, and is at most T (n,d-1,d-2)(3+O(n-1)) for fixed code dimension k=n-d+1. For d=3,4, we prove that the stopping redundancy of MDS codes is equal to T(n,d-1,d-2), for which exact formulas are known. For d=5, we show that the stopping redundancy of MDS codes is either T(n,4,3) or T(n,4,3)+1