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arXiv · 2501.11129

Optimal Binary Variable-Length Codes with a Bounded Number of 1's per Codeword: Design, Analysis, and Applications

Roberto Bruno·Roberto De Prisco·Ugo Vaccaro
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Abstract

In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity algorithm for the construction of such codes, where $n$ is the number of codewords. We also describe several scenarios where the need to design these kinds of codes naturally arises. We also provide a Kraft-like inequality for the existence of (optimal) variable-length binary codes, subject to the above-described constraint on the number of 1's in each codeword.

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Roberto Bruno, Roberto De Prisco, Ugo Vaccaro. 2025-01-19. Optimal Binary Variable-Length Codes with a Bounded Number of 1's per Codeword: Design, Analysis, and Applications. https://arxiv.org/abs/2501.11129

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