At the IEEE ISIT in Budapest in 1991 we agreed that Yuri would come to Eindhoven the next year. Supported by the Universiteitsfonds Eindhoven, whose chairman was Jack van Lint at that time, Yuri visited the Information Theory group in May 1992. We decided to investigate universal source coding algorithms for FSMX sources, like e.g. the method proposed by Rissanen in [5]. It was our idea that these algorithms were designed to have a good asymptotical behavior while the non-asymptotical performance, which is important in real life, was not very well understood.
After a while we realized that the idea of selecting relevant contexts was not a good one. This prevented researchers to determine the non-asymptotical behavior of their methods. An obvious alternative was weighting, an almost classical procedure. This way of thinking more or less immediately led to the context-tree weighting (CTW) algorithm.
The CTW algorithm follows from first principles and combines a desirable (asymptotical as well as non-asymptotical) performance with an extremely simple analysis. Therefore, when Michelle Effros asked us to write a ``reflections''-paper for the IT Newsletter, we decided to write a mini-course on ``universal source coding for tree sources'' which at the end focusses on the CTW algorithm. It is the content of the following sections.