  A green code attempts to minimize the total energy per-bit required to
communicate across a noisy channel. The classical information-theoretic
approach neglects the energy expended in processing the data at the encoder and
the decoder and only minimizes the energy required for transmissions. Since
there is no cost associated with using more degrees of freedom, the
traditionally optimal strategy is to communicate at rate zero.
  In this work, we use our recently proposed model for the power consumed by
iterative message passing. Using generalized sphere-packing bounds on the
decoding power, we find lower bounds on the total energy consumed in the
transmissions and the decoding, allowing for freedom in the choice of the rate.
We show that contrary to the classical intuition, the rate for green codes is
bounded away from zero for any given error probability. In fact, as the desired
bit-error probability goes to zero, the optimizing rate for our bounds
converges to 1.
