Two-way interference channels with jammers

Alice and Bob want to exchange information over an additive interference channel that also contains a malicious eavesdropper-jammer James who aims to disrupt this two-way communication. In the baseline model (motivated by wireless jamming scenarios), Alice and Bob transmit length-n q-arj encodings x_A and x_B respectively of their own messages. James observes the interference pattern z = x_A + x_B, and as a non-causal function of ζ and his knowledge of Alice and Bob's codebooks, chooses a jamming pattern s of power (Hamming weight) at most pn. Alice and Bob then both observe the interfered-jammed signal x_A + x_B + s, and aim to decode each others' messages despite the jamming pattern s. We demonstrate that in such a model, the fact of interference actually AIDS communication by allowing for communication to occur in each direction at a rate of 1 - H_q(p), i.e., the jammer can do no worse than act like 'random noise'.¹ Interestingly, neither linear codes nor random codes (as 'usually' defined) achieve this performance - we thus define and analyze a new class of codes we call linearish codes that do. We then extend our results to general q-avy additive-error channels with asymmetric jamming patterns (with potentially different powers) to Alice and Bob, and also demonstrate how to simultaneously ensure information-theoretic secrecy of both Alice and Bob's messages from James.