Some Properties of Entropy with Applications to Data-Compression

In this talk we will give three properties of the entropy of a stationary information source, and show how each leads to a data-compression scheme. The first property is the classical 'asymptotic equipartition property' or 'AEP'. The second is a new result which concerns the interval between successive occurrences of a particular string in the data stream. The third is a new bound of J. Ziv on the probability of a string on source outputs, in terms of the number of 'phrases' in a 'parsing' of the string into distinct phrases.