Optimal Single-Bit Relaying Strategies With Multi-Relay Diversity

Many emerging applications require multi-hop wireless relaying, for which reliability requirements increase packet retransmissions, amplifying latency across hops. Existing works mostly focus on the simple two-hop, single-relay setting and ignore spatial diversity that enables a destination to receive independent noisy copies of data from multiple relays in parallel to improve error performance. In this paper, we consider a single-bit source message and construct learning-rate-optimal, delay-constrained multi-hop schemes by jointly designing time-varying, distributed relay mapping functions with destination decoding strategies. The learning-rate-optimal scheme, however, requires channel and relaying knowledge, which limits practical implementation. With the aim of practical implementation, we have also considered several low-complexity relay and destination strategies and analyzed their performances under different combinations. Numerical comparisons show that none of the alternatives universally dominate, and the system designer thus has to carefully opt for the best suitable schemes depending on the channel conditions. Finally, we show that carefully coordinating many low-quality relay channels in parallel can vastly outperform having only one high-quality relay channel, which demonstrates the spatial diversity gains for the first time in the learning over parallel-relay setting.