The difficulty of modeling energy consumption in communication systems leads to challenges in energy harvesting (EH) systems, in which nodes scavenge energy from their environment. An EH receiver must harvest enough energy for demodulating and decoding. The energy required depends upon factors, like code rate and signal-to-noise ratio, which can be adjusted dynamically. We consider a receiver which harvests energy from ambient sources and the transmitter, meaning the received signal is used for both EH and information decoding. Assuming a generalized function for energy consumption, we maximize the total number of information bits decoded, under both average and peak power constraints at the transmitter, by carefully optimizing the power used for EH, power used for information transmission, fraction of time for EH, and code rate. For transmission over a single block, we find there exist problem parameters for which either maximizing power for information transmission or maximizing power for EH is optimal. In the general case, the optimal solution is a tradeoff of the two. For transmission over multiple blocks, we give an upper bound on performance and give sufficient and necessary conditions to achieve this bound. Finally, we give some numerical results to illustrate our results and analysis.