Finite rate distributed weight-balancing and average consensus over digraphs
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This paper proposes and analyzes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant to the directed nature of the graph edges. It is proved that the algorithm converges to a weight-balanced solution at sublinear rate. The analysis builds upon a new metric inspired by positional system representations, which characterizes the dynamics of information exchange over the network, and on a novel step-size rule. Building on this result, a novel distributed algorithm is proposed that solves the average consensus problem over digraphs, using, at each iteration, finite rate simplex communications between adjacent nodes-some bits for the weight balancing problem and others for the average consensus. Convergence of the proposed quantized consensus algorithm to the average of the unquantized node's initial values is proved, both almost surely and in the rth moment of the error, for all positive integers r. Finally, numerical results validate our theoretical findings.
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