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Tree sources

If a source is memoryless, each new source symbol is generated according to the same parameter tex2html_wrap_inline2689 . In a more complex situation we can assume that the parameter for generating the next symbol depends on the most recent source symbols. A tree source is a nice concept to describe such sources. A tree source consists of a set tex2html_wrap_inline2915 of suffixes that together form a tree (see figure 2). To each suffix (leaf) s in the tree there corresponds a parameter tex2html_wrap_inline2919 . The probability of the next source symbol being one depends on the suffix in tex2html_wrap_inline2915 of the semi-infinite sequence of past source symbols.

We clearly want to distinguish between parameters and model. The model is the mechanism that enables the parameters, i.e. the suffix set (or tree).

A context of a source symbol tex2html_wrap_inline2923 is a suffix of the semi-infinite sequence tex2html_wrap_inline2925 that precedes it.

Example:

   figure654
Figure 2: Tree source with parameters and model.

Let tex2html_wrap_inline2941 and tex2html_wrap_inline2943 , and tex2html_wrap_inline2945 then

eqnarray803

For each source symbol tex2html_wrap_inline2923 we start in the root of the tree (see figure 2) and follow a path determined by past symbols tex2html_wrap_inline2949 . We always end up in a leaf. There we find the parameter for generating tex2html_wrap_inline2923 .



Ramesh Rao
Fri May 2 08:36:00 PDT 1997