The Gaussian interference channel in the presence of a malicious jammer

This paper considers the two-user Gaussian interference channel in the presence of one or two adversarial jammers. Existing outer and inner bounds for the Gaussian interference channel are generalized in the presence of the jammer(s). We show that for certain problem parameters, precisely the same bounds hold, but with the noise variance increased by the received power of the jammer at each receiver. Thus, the jammers can do no better than to transmit Gaussian noise. For these problem parameters, this allows us to recover the half-bit theorem. Moreover, we show that, if the jammer has greater received power than the legitimate user, symmetrizability makes the capacity zero. The proof of the outer bound is straightforward, while the inner bound generalizes the Han-Kobayashi rate splitting scheme. As a novel aspect, the inner bound takes advantage of the common message acting as common randomness for the private message; hence, the jammer cannot symmetrize only the private codeword without being detected. We also prove a new version of a packing lemma for the Gaussian arbitrarily-varying channel.