Universal sequential coding of single messages (Q1112787)

We define coding redundancy of single messages. A coding method is proposed which ensures a uniform bound on this redundancy for all messages on the output of a source with unknown statistical properties. Using the same criterion, we investigate the possibilities of sequential coding of messages, including messages on the output of a source with unknown statistical properties. Upper bounds on redundancy are obtained for memoryless sources, Markov chains, and various sets of Markov sources.