Improved Probabilistic Bounds on Stopping Redundancy

For a linear code C, the stopping redundancy of C is defined as the minimum number of check nodes in a Tanner graph T for C such that the size of the smallest stopping set in T is equal to the minimum distance of C. Han and Siegel recently proved an upper bound on the stopping redundancy of general linear codes, using probabilistic analysis. For most code parameters, this bound is the best currently known. In this correspondence, we present several improvements upon this bound.