We investigate optimal power management (PM) policies for an Energy Harvesting Additive White Gaussian Noise (EH-AWGN) Channel from a transmitter to a receiver. The transmitter is equipped with an infinite size rechargeable battery. The transmitter is able to harvest energy from the environment to afford the required energy for data transmission. The arrival rate of the harvested energy is assumed to remain unchanged during each time frame, when a block code transmission occurs, and it varies independently and randomly across time frames (block codes) according to the Bernoulli distribution. The arrival energy sequence is assumed to be known causally at the transmitter. We achieve three novel simple policies as Lower Bounds (LBs) on the average throughput where the average is taken over the rates of L blocks. We prove that they are all optimal in an asymptotic sense as L grows to infinity. Comparing with the optimal offline policy for the similar model, where the arrival energy sequence is known non-causally at the transmitter, the proposed policies have low complexity and exhibit small tolerable inefficiency. As L grows, the achieved LBs meet the optimal offline average throughput. Hence, the policies can be employed as simple offline policies when L is sufficiently large.