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