An efficient algorithm for computing bounds on the average transmitted power in generalized partial response

An algorithm for computing bounds on the average transmitted power in generalized partial response signaling, also known as Tomlinson-Harashima (TH) precoding, is presented and its derivation is outlined. This algorithm requires knowledge of the marginal probability distributions of the input signal constellation, and is only appropriate when the domains of the marginal distributions are a subset of the set of even integers or a subset of the set of odd integers. These computed bounds are a generalization of the closed form bounds derived by Maze and Salt (1976) for symmetrical PAM constellations and rectangular QAM constellations with equally probable symbols