The Gaussian Interference Channel in the Presence of Malicious Jammers
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This paper considers the two-user Gaussian interference channel in the presence of adversarial jammers. We first provide a general model including an arbitrary number of jammers, and show that its capacity region is equivalent to that of a simplified model in which the received jamming signal at each decoder is independent. Next, existing outer and inner bounds for two-user Gaussian interference channel are generalized for this simplified jamming model. 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. In weak and strong interference regime, our inner bound matches the corresponding Han-Kobayashi bound with increased noise variance by the received power of the jammer, and even in strong interference we achieve the exact capacity. Furthermore, we determine the symmetric degrees of freedom where the signal-to-noise, interference-to-noise and jammer-to-noise ratios are all tend to infinity. 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. This complication requires an extra condition on the signal power, so that in general our inner bound is not identical to the Han-Kobayashi bound. We also prove a new variation of the packing lemma that applies for multiple Gaussian codebooks in an adversarial setting.
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