Admissibility Properties of Gilbert’s Encoding for Unknown Source Probabilities

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.