A geometric slicing lower bound for average-cost dynamic programming

A geometric slicing idea is proposed to lower bound infinite-horizon average-cost dynamic programs. The idea divides an infinite-horizon problem into finite-horizon ones with discounted cost. The idea is applied to control-over-communication-channel problems to find a fundamental limit of such systems. Lower bounds on the performance are given in terms of the capacity of the channel. The lower bounds are compared with explicit control strategies to provide quantitative and qualitative understanding about the strategies.