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A Lyapunov approach is developed to establish the convergence rates of discrete-time linear consensus. The approach combines the use a quadratic time-varying comparison function and an adjoint dynamics of the linear consensus dynamics. New convergence rate results are obtained that are characterized with an explicit dependence on the graph structure including the longest shortest path.
On a binary erasure channel (BEC) with erasing probability e, the performance of a binary linear code is determined by the incorrigible sets of the code. The incorrigible set distribution (ISD) {Ii}ni=0 enumerates the number of incorrigible sets with size i of the code. The probability of unsuccessful decoding under optimal decoding for the code could be formulated by the ISD and ε. In this paper,...
Recently, Dimakis, Smarandache, and Vontobel indicated that the parity-check matrices of good LDPC codes can be used as provably good measurement matrices for compressed sensing (CS) under basis pursuit (BP). In this paper, we consider the parity-check matrix H(r, q) of the array codes, one of the most important kind of structured LDPC codes. The spark, i.e. the smallest number of linearly dependent...
The knowledge and expertise of researchers and professors is the major asset that universities hold. In order to make use of this asset, it is necessary to share expertise between staff as well as transfer expertise to industry. Expertise matching - locating experts with the specific expertise is receiving more and more attention since it facilitates people connection to each other. This paper proposes...
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