Two-Way Gaussian Networks With a Jammer and Decentralized Control

McDonald, Curtis; Alajaji, Fady; Yüksel, Serdar

doi:10.1109/tcns.2019.2923385

“…In particular, the capacity is lower than what we would get if the noise vector were Gaussian. A game-theoretic version of the quadratically constrained case we study here was studied in [22].…”

Section: Introductionmentioning

confidence: 99%

Quadratically Constrained Two-way Adversarial Channels

Zhang

¹

,

Vatedka

²

,

Jaggi

³

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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We study achievable rates of reliable communication in a power-constrained two-way additive interference channel over the real alphabet where communication is disrupted by a power-constrained jammer. This models the wireless communication scenario where two users Alice and Bob, operating in the full duplex mode, wish to exchange messages with each other in the presence of a jammer, James. Alice and Bob simultaneously transmit their encodings x A and x B over n channel uses. It is assumed that James can choose his jamming signal s as a noncausal randomized function of x A `xB , and the codebooks used by Alice and Bob. Alice and Bob observe x A `xB `s, and must recover each others' messages reliably. In this article, we provide upper and lower bounds on the capacity of this channel which match each other and equal 1 2 log `1 2 `SNR ˘in the high-SNR regime (where SNR, signal to noise ratios, is defined as the ratio of the power constraints of the users to the power constraint of the jammer). We give a code construction based on lattice codes, and derive achievable rates for large SNR. We also present upper bounds based on two specific attack strategies for James. Along the way, sumset property of lattices for the achievability and general properties of capacity-achieving codes for memoryless channels for the converse are proved, which might be of independent interest. The full version of this paper is [1].

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“…In particular, the capacity is lower that what we would get if the noise vector were Gaussian. A game-theoretic version of the quadratically constrained case we study here was studied by McDonald et al [MAY19].…”

Section: Introductionmentioning

confidence: 99%

Quadratically Constrained Myopic Adversarial Channels

Zhang

¹

,

Vatedka

²

,

Jaggi

³

et al. 2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We study achievable rates of reliable communication in a power-constrained two-way additive interference channel over the real alphabet where communication is disrupted by a power-constrained jammer. This models the wireless communication scenario where two users Alice and Bob, operating in the full duplex mode, wish to exchange messages with each other in the presence of a jammer, James. Alice and Bob simultaneously transmit their encodings x A and x B over n channel uses. It is assumed that James can choose his jamming signal s as a noncausal randomized function of x A and x B , and the codebooks used by Alice and Bob. Alice and Bob observe x A`xB`s , and must recover each others' messages reliably. In this article, we provide upper and lower bounds on the capacity of this channel which match each other and equal 1 2 log`1 2`S NR˘in the high-SNR regime (where SNR, signal to noise ratios, is defined as the ratio of the power constraints of the users to the power constraint of the jammer). We give a code construction based on lattice codes, and derive achievable rates for large SNR. We also present upper bounds based on two specific attack strategies for James. Along the way, sumset property of lattices for the achievability and general properties of capacity-achieving codes for memoryless channels for the converse are proved, which might be of independent interest. 1 2 log`1 2`P N˘i s the capacity in high-SNR regime, we do not believe that this is tight in all regimes. Our intuition comes from the following improved converse result. We are able to push the boundary of zero-rate regime inward via certain symmetrization strategy which we call z-aware symmetrization.Theorem 5 (Converse). For a pP, N q quadratically constrained two-way adversarial channel, neither of the users can achieve positive rate if N ą 3P {4, or SNR ă 4{3.Again, the above theorem can be trivially generalized to the asymmetric case which reads as follows.Theorem 6 (Converse). For a pP A , P B , N A , N B q quadratically constrained two-way adversarial channel, user one cannot achieve positive rate if N A ą 2P B`PA 4

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