In this work, we explore the capacity of point-to-point fast fading channels in the presence of an adversary. We assume that the fading gains are known at the decoder; they may also be known to the encoder and/or adversary. If the adversary does not know the gains, then the capacity is equal to the capacity of the corresponding fading channel with the noise variance raised by the power of the jammer. If the gains are available at the jammer, then the capacity is determined by the worst-case noise variance as a function of the channel gain subject to the jammer's power constraint; if the jammer has enough power, then it can imitate the legitimate user's channel, causing the capacity to drop to zero.
In this work, we explore the capacity of point-to-point fast fading channels in the presence of an adversary. We assume that the fading gains are known at the decoder; they may also be known to the encoder and/or adversary. If the adversary does not know the gains, then the capacity is equal to the capacity of the corresponding fading channel with the noise variance raised by the power of the jammer. If the gains are available at the jammer, then the capacity is determined by the worst-case noise variance as a function of the channel gain subject to the jammer's power constraint; if the jammer has enough power, then it can imitate the legitimate user's channel, causing the capacity to drop to zero.
This paper considers an arbitrarily-varying fading channel consisting of one transmitter, one receiver and an arbitrarily varying adversary. The channel is assumed to have additive Gaussian noise and fast fading of the gain from the legitimate user to the receiver. We study four variants of the problem depending on whether the transmitter and/or adversary have access to the fading gains; we assume the receiver always knows the fading gains. In two variants the adversary does not have access to the gains, we show that the capacity corresponds to the capacity of a standard point-to-point fading channel with increased noise variance. The capacity of the other two cases, in which the adversary has knowledge of the channel gains, are determined by the worst-case noise variance as a function of the channel gain subject to the jammer's power constraint; if the jammer has enough power, then it can imitate the legitimate user's channel, causing the capacity to drop to zero. We also show that having the channel gains causally or non-causally at the encoder and/or the adversary does not change the capacity, except for the case where all parties know the channel gains. In this case, if the transmitter knows the gains non-causally, while the adversary knows the gains causally, then it is possible for the legitimate users to keep a secret from the adversary. We show that in this case the capacity is always positive.
This paper considers the two-user Gaussian arbitrarily-varying broadcast channel, wherein a power-limited transmitter wishes to send a message to each of two receivers. Each receiver sees a superposition of the transmitter's sequence, Gaussian noise, and a signal from a power-limited malicious jammer. The jammer is assumed to know the code, but is oblivious to real-time transmissions. The exact capacity region of this setting is determined to be the capacity region of the standard Gaussian broadcast channel, but with the noise variance increased by the power of the jammer, as long as the received power of the jammer at each receiver is less than that of the legitimate transmitter. A key aspect of the achievable scheme involves sharing randomness from the transmitter to the receivers by breaking the transmitted sequence into segments, and either transmitting at full power in a segment, or sending zero. By coding over the on/off signal, a small shared randomness can be established without corruption by the jammer, and without interfering with the standard superposition coding strategy for the Gaussian broadcast channel.
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.
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.
We study the Gaussian multiple access channel in presence of an adversary, who is simultaneously able to eavesdrop and jam, i.e., an active wiretapper. We assume that the adversary has a power constraint, which she can utilize to have any arbitrary jamming strategy. The multiple access channel between the legitimate transmitters and the receiver thus becomes arbitrarily varying. We derive inner and outer bounds on the secrecy rate region of our model. In the case of a degraded channel, we characterize the optimal secrecy sum-rate, and within 0.5 bits per channel use the optimal individual rate constraints. As a special case, we obtain the secrecy capacity of the point-to-point Gaussian wiretap channel when the eavesdropper is able to arbitrarily jam.
The arbitrarily varying channel can be modeled as communication in the presence of a jammer. In this paper we propose a new model: a jammer who knows the channel input, and where the transmitter and receiver share a secret random key. Shared randomness differentiates this scenario from the case where the jammer knows the message. For sufficiently large key rate, we determine the capacity of this channel (which may be strictly smaller than the case where the jammer knows only the message). We also provide an upper bound on the minimum key rate required to achieve capacity. We prove that additionally revealing the message to the jammer does not change the capacity, provided the key rate is sufficiently large. This new capacity result differs from existing results for the AVC, and in fact coincides with a well-known upper bound on the deterministic coding capacity of the AVC with maximum error. Without secret keys, our problem degenerates to deterministic coding for the AVC with maximum probability of error, a well-known hard problem. Our results demonstrate that knowledge of the channel input is better than knowledge of the message for the jammer.