Grid Topology Identification With Hidden Nodes via Structured Norm Minimization.

This letter studies a topology identification problem for an electric distribution grid using sign patterns of the inverse covariance matrix of bus voltage magnitudes and angles, while accounting for hidden buses. Assuming the grid topology is sparse and the number of hidden buses are fewer than those of the observed buses, we express the observed voltages inverse covariance matrix as the sum of three structured matrices: sparse matrix, low-rank matrix with sparse factors, and low-rank matrix. Using the sign patterns of the first two of these matrices, we develop an algorithm to identify the topology of a distribution grid with a minimum cycle length greater than three. To estimate the structured matrices from the empirical inverse covariance matrix, we formulate a novel convex optimization problem with appropriate sparsity and structured norm constraints and solve it using an alternating minimization method. We validate the proposed algorithm's performance on a modified IEEE 33 bus system.

List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel.

In this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power constraints. We also assume that there is no path between the adversary and the legitimate user but the adversary knows the legitimate user's code. We show that for any list size L, the capacity is equivalent to the capacity of a point-to-point Gaussian channel with noise variance increased by the adversary power, if the adversary has less power than L times the transmitter power; otherwise, the capacity is zero. In the converse proof, we show that if the adversary has enough power, then the decoder can be confounded by the adversarial superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof benefits from a novel variant of the Csiszár-Narayan method for the arbitrarily-varying channel.