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Traditional communication theory focuses on minimizing transmit power. However, communication links are increasingly operating at shorter ranges where transmit power can be significantly smaller than the power consumed in decoding. This paper models the required decoding power and investigates the minimization of total system power from two complementary perspectives. First, an isolated point-to-point link is considered. Using new lower bounds on the complexity of message-passing decoding, lower bounds are derived on decoding power. These bounds show that 1) there is a fundamental tradeoff between transmit and decoding power; 2) unlike the implications of the traditional "waterfall" curve which focuses on transmit power, the total power must diverge to infinity as error probability goes to zero; 3) Regular LDPCs, and not their known capacity-achieving irregular counterparts, can be shown to be power order optimal in some cases; and 4) the optimizing transmit power is bounded away from the Shannon limit. Second, we consider a collection of links. When systems both generate and face interference, coding allows a system to support a higher density of transmitter-receiver pairs (assuming interference is treated as noise). However, at low densities, uncoded transmission may be more power-efficient in some cases.