A major bottleneck of current integrated circuits is the performance of on-chip communication. It can be dramatically improved using wave-pipelining, which is very power efficient since it avoids additional pipeline registers. However, the error-free operation is getting challenging as technology scales down. Recently, approximate/stochastic communication is gaining interest since it allows to trade-off transmission quality by performance/power in resilient applications such as machine learning. Taking into account the challenges of classical wave-pipelining, this brief proposes the concept of stochastic wave-pipelining communication. A comprehensive experimental result using a 65 nm commercial technology evaluates the proposed communication technique. Furthermore, the proposed approach is assessed using a case study employing Optical Character Recognition (OCR).