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In this paper, we consider a three node relay network comprising a source, arelay, and a destination. The source transmits the message to the destinationusing hybrid automatic repeat request (HARQ) with incremental redundancy (IR).The relay overhears the transmitted message, amplifies it using a variable gainamplifier, and then forwards the message to the destination. This lattercombines both the source and the relay message and tries to decode theinformation. In case of decoding failure, the destination sends a negativeacknowledgement. A new replica of the message containing new parity bits isthen transmitted in the subsequent HARQ round. This process continues untilsuccessful decoding occurs at the destination or a maximum number $M$ of roundsis reached. We study the performance of HARQ-IR over the considered relaychannel from an information theoretic perspective. We derive exact expressionsand bounds for the information outage probability, the average number oftransmissions, and the average transmission rate. Moreover, we evaluate thedelay experienced by Poisson arriving packets over the considered relaynetwork. We also provide analytical expressions for the expected waiting time,the sojourn time, and the energy efficiency. The derived exact expressions arevalidated by Monte Carlo simulations.

Performance Analysis of Hybrid ARQ with Incremental Redundancy over Amplify-and-Forward Dual-Hop Relay Channels