  This paper characterizes an achievable information-energy region of
simultaneous information and energy transmission over an additive white
Gaussian noise channel. This analysis is performed in the finite block-length
regime with finite constellations. More specifically, a method for constructing
a family of codes is proposed and the set of achievable tuples of information
rate, energy rate, decoding error probability (DEP) and energy outage
probability (EOP) is characterized. Using existing converse results, it is
shown that the construction is information rate, energy rate, and EOP optimal.
The achieved DEP is, however, sub-optimal.
