  We revisit the problem of minimal local grammar-based coding. In this
setting, the local grammar encoder encodes grammars symbol by symbol, whereas
the minimal grammar transform minimizes the grammar length in a preset class of
grammars as given by the length of local grammar encoding. It has been known
that such minimal codes are strongly universal for a strictly positive entropy
rate, whereas the number of rules in the minimal grammar constitutes an upper
bound for the mutual information of the source. Whereas the fully minimal code
is likely intractable, the constrained minimal block code can be efficiently
computed. In this article, we present a new, simpler, and more general proof of
strong universality of the minimal block code, regardless of the entropy rate.
The proof is based on a simple Zipfian bound for ranked probabilities. By the
way, we also show empirically that the number of rules in the minimal block
code cannot clearly discriminate between long-memory and memoryless sources,
such as a text in English and a random permutation of its characters. This
contradicts our previous expectations.
