Quadratically Constrained Myopic Adversarial Channels

TL;DR

This paper characterizes the capacity of quadratically constrained myopic adversarial channels under various noise-to-signal ratios, introducing novel decoding and attack techniques, and explores secrecy capacity with eavesdropping adversaries.

Contribution

It provides the first capacity characterization for these channels under different NSR regimes, using new list-decoding and attack methods, and extends to secrecy capacity bounds.

Findings

Capacity characterized for certain NSR regimes with deterministic encoding.

Capacity determined with limited common randomness in other regimes.

Introduces a novel myopic list-decoding technique and a Plotkin-type push attack.

Abstract

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 which may be of independent interest. We also give bounds on the secrecy capacity of this channel assuming that the jammer is simultaneously eavesdropping.