Stochastic-Adversarial Channels : Online Adversaries With Feedback Snooping

TL;DR

This paper investigates the capacity of online adversarial channels with feedback snooping, providing complete capacity results for erasures and bounds for bit-flips in mixed noise models.

Contribution

It offers the first comprehensive capacity characterization for causal adversaries with feedback in erasure channels and bounds for flip channels in stochastic-adversarial models.

Findings

Complete capacity characterization for erasure channels with feedback.

Bounds on capacity for flip channels with causal adversaries.

Insights into the impact of feedback snooping on adversarial channel capacity.

Abstract

The growing need for reliable communication over untrusted networks has caused a renewed interest in adversarial channel models, which often behave much differently than traditional stochastic channel models. Of particular practical use is the assumption of a \textit{causal} or \textit{online} adversary who is limited to causal knowledge of the transmitted codeword. In this work, we consider stochastic-adversarial mixed noise models. In the set-up considered, a transmit node (Alice) attempts to communicate with a receive node (Bob) over a binary erasure channel (BEC) or binary symmetric channel (BSC) in the presence of an online adversary (Calvin) who can erase or flip up to a certain number of bits at the input of the channel. Calvin knows the encoding scheme and has causal access to Bob's reception through \textit{feedback snooping}. For erasures, we provide a complete capacity characterization with and without transmitter feedback. For bit-flips, we provide interesting converse and achievability bounds.