On the Stopping Distance and Stopping Redundancy of Finite Geometry LDPC Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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
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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The stopping redundancy of the code is an important parameter which arises from analyzing the performance of a linear code under iterative decoding on a binary erasure channel. In this paper, we will consider the stopping redundancy of Reed-Muller codes and related codes. Let R(lscr,m) be the Reed-Muller code of length 2m and order lscr. Schwartz and Vardy gave a recursive construction of parity-check matrices for the Reed-Muller codes, and asked whether the number of rows in those parity-check matrices is the stopping redundancy of the codes. We prove that the stopping redundancy of R(m-2,m), which is also the extended Hamming code of length 2m, is 2m-1 and thus show that the recursive bound is tight in this case. We prove that the stopping redundancy of the simplex code equals its redundancy. Several constructions of codes for which the stopping redundancy equals the redundancy are discussed. We prove an upper bound on the stopping redundancy of R(1,m). This bound is better than the known recursive bound and thus gives a negative answer to the question of Schwartz and Vardy