Quadratically Constrained Two-way Adversarial Channels

We study achievable rates of reliable communication in a power-constrained two-way additive interference channel over the real alphabet where communication is disrupted by a power-constrained jammer. This models the wireless communication scenario where two users Alice and Bob, operating in the full duplex mode, wish to exchange messages with each other in the presence of a jammer, James. Alice and Bob simultaneously transmit their encodings $ \underline{x}_A $ and $\underline{x}_B $ over $ n $ channel uses. It is assumed that James can choose his jamming signal $ \underline{s} $ as a noncausal randomized function of $ \underline{x}_A $ and $ \underline{x}_B $, and the codebooks used by Alice and Bob. Alice and Bob observe $ \underline{x}_A+\underline{x}_B +\underline{s}$, and must recover each others' messages reliably. In this article, we give upper and lower bounds on the capacity of this channel which match each other in the high-$\mathsf{SNR}$ (signal to noise ratios, defined as the ratio of the power constraints of the users to the power constraint of the jammer) regime. We give a code construction based on lattice codes, and derive achievable rates for large $\mathsf{SNR}$. We also present upper bounds based on two specific attack strategies for James. For the converse, we also derive general properties of capacity-achieving codes for memoryless channels, which might be of independent interest.