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.