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Outage probability in an energy harvesting (EH) block-fading communication system is studied in the finite-horizon online setting. First, the offline version of the problem is considered, and formulated as a mixed integer linear program (MILP). Then, the infinite-horizon online problem (IIL) is considered relaxing the battery constraints. Solutions of these two problems provide lower bounds on the finite-horizon online problem, for which we provide a low-complexity heuristic scheme, called thedoi:10.1109/lcomm.2016.2641418 fatcat:4wlka3nbdjfkpocumwltypfh4q