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The throughput benefits of random linear network codes have been studiedextensively for wirelined and wireless erasure networks. It is often assumedthat all nodes within a network perform coding operations. Inenergy-constrained systems, however, coding subgraphs should be chosen tocontrol the number of coding nodes while maintaining throughput. In this paper,we explore the strategic use of network coding in the wireless packet erasurerelay channel according to both throughput and energy metrics. In the relaychannel, a single source communicates to a single sink through the aid of ahalf-duplex relay. The fluid flow model is used to describe the case where boththe source and the relay are coding, and Markov chain models are proposed todescribe packet evolution if only the source or only the relay is coding. Inaddition to transmission energy, we take into account coding and receptionenergies. We show that coding at the relay alone while operating in a ratelessfashion is neither throughput nor energy efficient. Given a set of systemparameters, our analysis determines the optimal amount of time the relay shouldparticipate in the transmission, and where coding should be performed.

Whether and Where to Code in the Wireless Relay Channel