If a source is memoryless, each new source symbol is generated
according to the same parameter
.
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
of suffixes that together form a
tree (see figure 2).
To each suffix (leaf) s in the tree there corresponds a parameter
.
The probability of the next source symbol being one depends on the
suffix in
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
is a suffix of the semi-infinite
sequence
that precedes it.
Example:
Figure 2: Tree source with parameters and model.
Let
and
,
and
then
For each source symbol
we start in the root of the tree (see
figure 2) and follow a path determined by past symbols
. We always end up in a leaf. There we find
the parameter for generating
.