  Designing distributed, fast and reliable wireless consensus protocols is
instrumental in enabling mission-critical decentralized systems, such as
robotic networks in the industrial Internet of Things (IIoT), drone swarms in
rescue missions, and so forth. However, chasing both low-latency and
reliability of consensus protocols is a challenging task. The problem is
aggravated under wireless connectivity that may be slower and less reliable,
compared to wired connections. To tackle this issue, we investigate fundamental
relationships between consensus latency and reliability through the lens of
wireless connectivity, and co-design communication and consensus protocols for
low-latency and reliable decentralized systems. Specifically, we propose a
novel communication-efficient distributed consensus protocol, termed Random
Representative Consensus (R2C), and show its effectiveness under gossip and
broadcast communication protocols. To this end, we derive a closed-form
end-to-end (E2E) latency expression of the R2C that guarantees a target
reliability, and compare it with a baseline consensus protocol, referred to as
Referendum Consensus (RC). The result shows that the R2C is faster compared to
the RC and more reliable compared when co-designed with the broadcast protocol
compared to that with the gossip protocol.
