Degrees of Freedom of Two-Hop Wireless Networks: "Everyone Gets the Entire Cake"

We show that fully connected two-hop wireless networks with K sources, K relays and K destinations have K degrees of freedom both in the case of time-varying channel coefficients and in the case of constant channel coefficients (in which case the result holds for almost all values of constant channel coefficients). Our main contribution is a new achievability scheme which we call Aligned Network Diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. In addition, we extend our scheme to multi-hop networks with fully connected hops, and multi-hop networks with MIMO nodes, for which the degrees of freedom are also fully characterized.Comment: Presented at the 2012 Allerton Conference. Submitted to IEEE Transactions on Information Theor

Dirty Paper Arbitrarily Varying Channel with a State-Aware Adversary

In this paper, we take an arbitrarily varying channel (AVC) approach to examine the problem of writing on a dirty paper in the presence of an adversary. We consider an additive white Gaussian noise (AWGN) channel with an additive white Gaussian state, where the state is known non-causally to the encoder and the adversary, but not the decoder. We determine the randomized coding capacity of this AVC under the maximal probability of error criterion. Interestingly, it is shown that the jamming adversary disregards the state knowledge to choose a white Gaussian channel input which is independent of the state