Statistical Power Allocation and Coded Bit Allocation Optimization in Mercury/Waterfilling

Motivated by statistical Waterfilling, we derive statistical Mercury/Waterfilling (M/WF) for both fixed average power and fixed average rate as the infinite time limit of the spatio-temporal M/WF solution. The M → ∞ limit of the conditional mean estimate (CME) receiver for unit-energy M-QAM constellations is derived, which may be used as a low complexity approximate CME estimate for dense QAM constellations. The asymptotic CME result is used to analytically characterize an upper bound on the mutual information properties of QAM. We develop a tree-search algorithm to efficiently optimize coded bit allocation in M/WF. Two analytical tests are derived to eliminate sub-trees of the graph.