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On the Maximum Size of a Prefix Code | IEEE Journals & Magazine | IEEE Xplore

On the Maximum Size of a Prefix Code


Abstract:

A prefix code minimal with respect to a bitstring x is a prefix code where x is a concatenation of its codewords and it is minimal with respect to this property. ...Show More

Abstract:

A prefix code minimal with respect to a bitstring x is a prefix code where x is a concatenation of its codewords and it is minimal with respect to this property. What is the maximum size M(n) among all minimal codes over all bitstrings of length n? In this paper we determine the value of M(n) for all natural numbers n , discuss its computational complexity, relation to the Lambert function, provide tight upper bounds, and describe how the value of M(n) enables one to construct efficiently a Huffman code in the case of uniform probability distribution of the codewords.
Published in: IEEE Transactions on Information Theory ( Volume: 69, Issue: 5, May 2023)
Page(s): 2855 - 2859
Date of Publication: 13 January 2023

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