Version 5.0 The LEDA User Manual

9.3 Prediction by Partial Matching ( PPMIICoder )
1. Definition
The PPMIICoder is based on the compression scheme “Prediction by Partial Matching
with Information Inheritance” by D. Shkarin [81].
This coder works as follows: Suppose we have processed the first n−1 symbols x 1 . . . x n−1
of the stream. Before reading the next symbol x n we try to guess it, i.e. for every symbol
s we estimate the probability p(s) for the event “x n = s”. This probability distribution
determines how the next symbol is encoded: The higher p(s), the fewer bits are used for
encoding s. If our estimation is good, which means that p(x n ) is high, then we obtain a
good compression rate.
In order to predict the probality distribution for the nth symbol the PPM approach
considers the preceding k symbols x n−k . . . x n−1 . We call these symbols the context of x n
and k the order of the model. (For k = 0 we obtain the order-0 model from the previous
section.) E.g., if the current context is “req”, then we should predict the letter “u” as
next symbol with high probability.
PPMII is a variant of PPM which usually achieves very accurate estimations.
The PPMIICoder combines very good compression rates with acceptable speed. (Shkarin
[81] reports that his coder outperforms ZIP and BZIP2 with respect to compression rates
and speed.) The only disadvantage of this coder is that it needs a fair amount of main
memory to store the model. However, the user can set an upper bound on the memory
usage. And he can specify which model restoration method the coder shall apply when it
runs out of memory:
• mr restart (default):
The model is deleted completely and rebuilt from scratch. This method is fast.
• mr cut off :
Parts of the model are freed to gain memory. This method is optimal for so-called
quasistationary sources. It usually gives better compression but it is slower.
• mr freeze:
The model is not extended any more. This method is optimal for so-called stationary
sources. (We want to point out that data streams arising in practical applications
usually do not behave like a stationary source.)
#include < LEDA/coding/PPMII.h >
2. Types
PPMIICoder :: mr method { mr restart, mr cut off, mr freeze }
the different model restoration modes.