Universal coding of zipf distributions

The universal coding of Zipf distributions are discussed. Coding schemes whose redundancy increases slower than n are known as universal. The universal coding scheme can be considered as an algorithm for combining expert advice whose code length is equal to the cumulative log loss and the redundancy is the difference between the loss of the combining algorithm and the loss of the best expert. When compressing natural-language text, it is reasonable to code the text a word at a time, thereby relying on the distribution of the words. One approach to reduce the redundancy in that case would be to restrict the collection of possible distributions over the words.