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In this paper, the fundamental limits on the rates at which information andenergy can be simultaneously transmitted over an additive white Gaussian noisechannel are studied under the following assumptions: $(a)$ the channel ismemoryless; $(b)$ the number of channel input symbols (constellation size) andblock length are finite; and $(c)$ the decoding error probability (DEP) and theenergy outage probability (EOP) are bounded away from zero. In particular, itis shown that the limits on the maximum information and energy transmissionrates; and the minimum DEP and EOP, are essentially set by the type induced bythe code used to perform the transmission. That is, the empirical frequencywith which each channel input symbol appears in the codewords. Using thisobservation, guidelines for optimal constellation design for simultaneousenergy and information transmission are presented.

Simultaneous Information and Energy Transmission with Finite Constellations