Harnessing HARQ Retransmissions for Fast Average Consensus Over Unreliable Communication Channels

In this work, we introduce a new consensus mechanism by incorporating a Hybrid Repeat reQuest (HARQ) error control protocol into the Ratio Consensus (RC) algorithm to achieve fast discrete-time asymptotic average consensus in the presence of packet retransmissions (information delays), and packet-dropping links (information loss) over directed networks. Using this consensus mechanism (hereinafter referred to as HARQ-RC), each transmitting node decides whether to retransmit packets (containing values of consensus variables) to its out-neighbors by utilizing their HARQ feedback signals. Under this protocol, each receiving node may detect the corrupted part of the received packet, and by combining successfully received information from previous retransmission trials, it may recover the information of the packet. This mechanism leads in a lower number of retransmission trials compared to standard ARQ mechanism, and hence the consensus iterations converge faster to the average consensus value. By introducing the weighted adjacency matrix that models the HARQ-based information exchange between nodes, we show that the nodes are guaranteed to reach asymptotic average consensus using the HARQ-RC mechanism despite the information delays and losses. The effectiveness of the HARQ-RC over bad communication links, with respect to achieving faster convergence to the average consensus value, is demonstrated under different simulation scenarios_