Admissibility properties or Gilbert´s encoding for unknown source probabilities (Corresp.)

Huffman coding provides optimal source encoding for events of specified source probabilities. Gilbert has proposed a scheme for source encoding when these source probabilities are imperfectly known. This correspondence shows that Gilbert´s scheme is a Bayes scheme against a certain natural prior distribution on the source probabilities. Consequently, since this prior distribution has nonzero mass everywhere, Gilbert´s scheme is admissible in the sense that no source encoding has lower average code length for every choice of source probabilities.