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This paper proposes the first distributed algorithm that solves theweight-balancing problem using only finite rate and simplex communicationsamong nodes, compliant with the directed nature of the graph edges. It isproved that the algorithm converges to a weight-balanced solution at sublinearrate. The analysis builds upon a new metric inspired by positional systemrepresentations, which characterizes the dynamics of information exchange overthe network, and on a novel step-size rule. Building on this result, a noveldistributed algorithm is proposed that solves the average consensus problemover digraphs, using, at each timeslot, finite rate simplex communicationsbetween adjacent nodes -- some bits for the weight-balancing problem and othersfor the average consensus. Convergence of the proposed quantized consensusalgorithm to the average of the node's unquantized initial values isestablished, both almost surely and in the moment generating function of theerror; and a sublinear convergence rate is proved for sufficiently largestep-sizes. Numerical results validate our theoretical findings.

Finite rate distributed weight-balancing and average consensus over digraphs