Quadratically Constrained Myopic Adversarial Channels

We study communication in the presence of a jamming adversary where quadratic power constraints are imposed on the transmitter and the jammer. The jamming signal is allowed to be a function of the codebook, and a noncausal but noisy observation of the transmitted codeword. For a certain range of the noise-to-signal ratios (NSRs) of the transmitter and the jammer, we are able to characterize the capacity of this channel under deterministic encoding or stochastic encoding, i.e., with no common randomness between the encoder/decoder pair. For the remaining NSR regimes, we determine the capacity under the assumption of a small amount of common randomness (at most 2 log (n) bits in one sub-regime, and at most Omega(n) bits in the other sub-regime) available to the encoder-decoder pair. Our proof techniques involve a novel myopic list-decoding result for achievability, and a Plotkin-type push attack for the converse in a subregion of the NSRs, both of which may be of independent interest. We also give bounds on the strong secrecy capacity of this channel assuming that the jammer is simultaneously eavesdropping.

Automated summary

In this study, we investigate communication in the presence of a jamming adversary with quadratic power constraints on the transmitter and the jammer. We characterize the capacity of this channel under different noise-to-signal ratios (NSRs) and discuss the assumption of common randomness between the encoder and decoder. Our proof techniques involve a myopic list-decoding result and a Plotkin-type push attack.