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In this paper the connection between the self-information of a source letter from a finite alphabet and its code-word length in a Huffman code is investigated. Consider the set of all independent finite alphabet sources which contain a source letter a of probabilityp. The maximum over this set of the length of a Huffman codeword for a is determined. This maximum remains constant aspvaries between the reciprocal values of two consecutive Fibonacci numbers. For the smallpthis maximum is approximately equal to[ log₂ {1+ √5}{2} ]⁻¹ ≈ 1.44times the self-information.
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Katona et al. (1976) studied this question.
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