On the minimum rate for strong universal block coding of a class of ergodic sources

For a class of ergodic sources
\Lambda
on a given finite alphabet satisfying certain conditions, a formula is given for the minimum rate above which strong universal fixed-rate and variable-rate block coding of
\Lambda
with respect to an arbitrary single-letter fidelity criterion can be done. The result extends several previous strong universal block coding theorems. As an application it is shown that there is a metric on the class of stationary sources weaker than
\bar{d}
-metric for which compactness of
\Lambda
in the metric implies that strong universal coding can be done at all rates.