For countably infinite alphabets, optimal prefix code lengths for the most probable symbol are fixed by intervals on its probability p1, and a low-information criterion identifies distributions whose lengths follow the pattern l_i = i.
Humblet,Optimal source coding for a class of integer alphabets (Corresp.), IEEE Transactions on Information Theory, vol
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About Optimal Prefix Codes over Countably Infinite Alphabets: Probabilistic Intervals for the Codeword Lengths Assignment
For countably infinite alphabets, optimal prefix code lengths for the most probable symbol are fixed by intervals on its probability p1, and a low-information criterion identifies distributions whose lengths follow the pattern l_i = i.