Shannon Information and Kolmogorov Complexity

The elementary theories of Shannon information and Kolmogorov complexity are cmpared, the extent to which they have a common purpose, and where they are fundamentally different. The focus is on: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new. Contents

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Peter Grünwald, Paul M. B. Vitányi
• Keywords: CORR 2004, Education, Kolmogorov Complexity, Sufficient Statistic, Versus Kolmogorov Complexity