The throughput benefits of random linear network codes have been studied
extensively for wirelined and wireless erasure networks. It is often assumed
that all nodes within a network perform coding operations. In
energy-constrained systems, however, coding subgraphs should be chosen to
control the number of coding nodes while maintaining throughput. In this paper,
we explore the strategic use of network coding in the wireless packet erasure
relay channel according to both throughput and energy metrics. In the relay
channel, a single source communicates to a single sink through the aid of a
half-duplex relay. The fluid flow model is used to describe the case where both
the source and the relay are coding, and Markov chain models are proposed to
describe packet evolution if only the source or only the relay is coding. In
addition to transmission energy, we take into account coding and reception
energies. We show that coding at the relay alone while operating in a rateless
fashion is neither throughput nor energy efficient. Given a set of system
parameters, our analysis determines the optimal amount of time the relay should
participate in the transmission, and where coding should be performed.Comment: 11 pages, 12 figures, to be published in the IEEE JSAC Special Issue
on Theories and Methods for Advanced Wireless Relay