Properties of optimal prefix-free machines as instantaneous codes

Details Properties of optimal prefix-free machines as instantaneous codes Properties of optimal prefix-free machines as instantaneous codes

2010-07-25

arxiv.org/abs/1007.4294v1

Computer Science

Information Theory

5 pages, no figures, final manuscript to appear in the Proceedings of the 2010 IEEE Information Theory Workshop, Dublin, Irela

Scientific paper

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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