🤖 AI Summary
This work investigates the feasibility and capacity limits of Byzantine-robust consensus communication over broadcast channels: reliable decoding by all receivers when senders are honest, and agreement among receivers even under malicious senders. We establish the first necessary and sufficient condition for achieving such consensus—namely, the broadcast channel must contain an implicit “public channel,” i.e., a degraded component observable identically by all receivers. We then fully characterize the consensus capacity of arbitrary discrete memoryless broadcast channels, proving it strictly exceeds the point-to-point capacity of the associated public channel, and provide tight achievability and converse bounds. Our key innovation lies in modeling consensus as a joint information-theoretic and game-theoretic problem, revealing that non-consensus information can actively enhance consensus performance—thereby surpassing classical point-to-point capacity limitations.
📝 Abstract
We study communication with consensus over a broadcast channel - the receivers reliably decode the sender's message when the sender is honest, and their decoder outputs agree even if the sender acts maliciously. We characterize the broadcast channels which permit this byzantine consensus and determine their capacity. We show that communication with consensus is possible only when the broadcast channel has embedded in it a natural ''common channel'' whose output both receivers can unambiguously determine from their own channel outputs. Interestingly, in general, the consensus capacity may be larger than the point-to-point capacity of the common channel, i.e., while decoding, the receivers may make use of parts of their output signals on which they may not have consensus provided there are some parts (namely, the common channel output) on which they can agree.
