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arXiv · 1007.4294

Properties of optimal prefix-free machines as instantaneous codes

Kohtaro Tadaki
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Abstract

The optimal prefix-free machine U is a universal decoding algorithm used to define the notion of program-size complexity H(s) for a finite binary string s. Since the set of all halting inputs for U is chosen to form a prefix-free set, the optimal prefix-free machine U can be regarded as an instantaneous code for noiseless source coding scheme. In this paper, we investigate the properties of optimal prefix-free machines as instantaneous codes. In particular, we investigate the properties of the set U^{-1}(s) of codewords associated with a symbol s. Namely, we investigate the number of codewords in U^{-1}(s) and the distribution of codewords in U^{-1}(s) for each symbol s, using the toolkit of algorithmic information theory.

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Kohtaro Tadaki. 2010-07-25. Properties of optimal prefix-free machines as instantaneous codes. https://doi.org/10.1109/cig.2010.5592776

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