Stochastic-Adversarial Channels : Online Adversaries With Feedback Snooping

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.