  We provide a mutual information lower bound that can be used to analyze the
effect of training in models with unknown parameters. For large-scale systems,
we show that this bound can be calculated using the difference between two
derivatives of a conditional entropy function. The bound does not require
explicit estimation of the unknown parameters. We provide a step-by-step
process for computing the bound, and provide an example application. A
comparison with known classical mutual information bounds is provided.
