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PPM(Prediction by Partial Match)
The Huffman and arithmetic coders are sometimes referred to as the
entropy coder
.
These methods normally use an order (0) model. If a good model with low entropy can be
built external to the algorithms, these algorithms can generate the binary codes very
efficiently. One of the most well known modeler is
“
prediction by partial match” (PPM
)
[ClW84; Moff90].
PPM uses a finite context Order (
k
) model where
k
is the maximum context that is
specified ahead of execution of the algorithm. The program maintains all the previous
occurrences of context at each level of
k
in a table or a trielike data structure with
associated probability values for each context.
Exclusion Principle
: If a context at a lower level is a suffix of a context at a higher level,
this context is excluded at the lower level.
Escape Character
: At each level and for each distinct context at that level (except the
level with
k
= 1), an
escape character
is defined whose frequency of occurrence is
assumed to be equal to the number of distinct characters occurring for a given context
encountered in the text so far encoded, at that context level for the purpose of calculating
its probability. The escape character is required to handle the situation when the encoder
encounters a new context never encountered before at any context level to give the
decoder a signal that the context length has to be reduced by 1.
Algorithm
: During the encoding process, the algorithm estimates the probability of the
occurrence of some given
next character
in the text stream as follows: the algorithm tries
to find the current context of maximum length
k
for this character in the context table or
trie. If the context is not found, it passes the probability of the escape character at this
level for this context and goes down one level to
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 Spring '11
 Mukherjee

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