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arXiv:1712.04133

The Gaussian Interference Channel in the Presence of Malicious Jammers

Fatemeh Hosseinigoki, Oliver Kosut

Published Dec 12, 2017• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1712.04133

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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.
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.
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We introduce a secure communication setup of an interference channel whose transmitted signals are fed into interleavers. The interleavers apply random permutations to the signals, and the realizations of the permutations are made known to the receivers but not the transmitters. This communication setup can also model a situation in which the encoders are ignorant of the codebooks of one another, while the decoders are cognizant of the codebooks. We study the capacity region of a two-user secure Z-interference channel, and prove that an asymptotically optimal strategy of the interfered user is to use a constant composition random code. Consequently we establish the result that the capacity region of this channel, in the weak interference regime, is obtained by the Han-Kobayashi coding scheme. Further, we present an outer bound for the secure additive doubly weak interference channel, and an outer bound on the capacity region of the secure additive interference channel with mixed interference.
We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. For the symmetric case, this simple scheme is optimal when the interference-to-signal ratio (all link strengths in decibel scale) is no more than 2/3. However, when the ratio is more than 2/3, we show that this simple scheme is not optimal anymore and a scheme with cooperative jamming is proposed to achieve the optimal secure sum generalized degrees-of-freedom (GDoF). Specifically, for the symmetric case, we complete the optimal secure sum GDoF characterization for all the interference regimes, for almost all channel gains (except for a set of channel gains of measure zero).
We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. For the symmetric case, this simple scheme is optimal when the interference-to-signal ratio (all link strengths in decibel scale) is no more than 2/3. However, when the ratio is more than 2/3, we show that this simple scheme is not optimal anymore and a scheme with cooperative jamming is proposed to achieve the optimal secure sum generalized degrees-of-freedom (GDoF). Specifically, for the symmetric case, we complete the optimal secure sum GDoF characterization for all the interference regimes.