Consensus Capacity of Noisy Broadcast Channels

TL;DR

This paper characterizes the types of noisy broadcast channels that enable reliable consensus among receivers, even in the presence of malicious actors, and determines the maximum achievable rate for such consensus communication.

Contribution

It introduces the concept of a 'common channel' within broadcast channels necessary for consensus and derives the capacity limits for consensus communication over noisy channels.

Findings

Consensus is possible only with a natural 'common channel' embedded in the broadcast.

Consensus capacity can exceed the point-to-point capacity of the common channel.

Receivers can utilize parts of their outputs without consensus if the common channel output is reliable.

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.