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Posted 11 Jun 2001


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Using PPMD for compression

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11 Jun 20014 min read
This article presents a class for using PPM to compress a file.

Sample Image - ppmd_demo.gif

Theoretical Background

(from Unbounded length contexts for PPM by John G. Cleary, W. J. Teahan, Ian H. Witten

Prediction by partial matching, or PPM, is a finite­context statistical modeling technique that can be viewed as blending together several fixed­order context models to predict the next character in the input sequence. Prediction probabilities for each context in the model are calculated from frequency counts which are updated adaptively; and the symbol that actually occurs is encoded relative to its predicted distribution using arithmetic coding. The maximum context length is a fixed constant, and it has been found that increasing it beyond about six or so does not generally improve compression.

The basic idea of PPM is to use the last few characters in the input stream to predict the upcoming one. Models that condition their predictions on a few immediately preceding symbols are called finite­context models of order k, where k is the number of preceding symbols used. PPM employs a suite of fixed­order context models with different values of k, from 0 up to some pre­determined maximum, to predict upcoming characters.

For each model, a note is kept of all characters that have followed every length­k subsequence observed so far in the input, and the number of times that each has occurred. Prediction probabilities are calculated from these counts. The probabilities associated with each character that has followed the last k characters in the past are used to predict the upcoming character. Thus from each model, a separate predicted probability distribution is obtained.

These distributions are effectively combined into a single one, and arithmetic coding is used to encode the character that actually occurs, relative to that distribution. The combination is achieved through the use of escape probabilities. Recall that each model has a different value of k. The model with the largest k is, by default, the one used for coding. However, if a novel character is encountered in this context, which means that the context cannot be used for encoding it, an escape symbol is transmitted to signal the decoder to switch to the model with the next smaller value of k. The process continues until a model is reached in which the character is not novel, at which point it is encoded with respect to the distribution predicted by that model. To ensure that the process terminates, a model is assumed to be present below the lowest level, containing all characters in the coding alphabet. This mechanism effectively blends the different order models together in a proportion that depends on the values actually used for escape probabilities.


PPMD_Coder is based on PPMD var E by Dmitri Shkarin. You can download the original code here.

I have created a static library around it and an easy to use wrapper class. The constructor expects 4 parameters:

  • The name of the Input file
  • The name of the Output file. If empty or NULL and you Compress a file the extension ".ppm" will be added, if you Uncompress a file the name stored in the compressed file will be used.
  • The memory in MBytes (between 1 and 256) which can be used by the program. It will be dynamically allocated on the heap so don't use unrealistic values. After compression you can look at the statistic to see how much memory was used. It's a good idea to keep the value as low as possible because for decompression the same amount of memory must be allocated or decompression will fail.
  • The Order size (between 2 and 16). A value of 6 is a good starting point but it's worth trying out higher values.
  • The memory and order size can also be set later with OrderSize and SubAllocatorSize. Values which are out of range are adjusted, the return value is the size actually set. They have only impact on the compression.

    Now you can decide what to do: call Compress or Uncompress. Both throw an exception when an error occurs. Additionally they return TRUE on success or FALSE. Here is an example:

    #include "ppmd_coder.h"
    // Use default values: output name will get the extension "ppm",
    // MemorySize is 8 and OrderSize is 6
    PPMD_Coder ppmd(szInput);
        // Without exceptions you would check the return value.
        // File is compressed now 
        // Get some statistic:
        DWORD m1, m2;
        ppmd.GetMemoryUsage(m1, m2);
        // m1 = used memory only MBytes 
        // m2 = used memory only bytes below 1 MBytes 
        TRACE(_T("Memory used:       %i.%i MBytes\n"), m1, m2);
        TRACE(_T("Compression ratio: %2.2f\n"), ppmd.GetRatio());
    catch (exception &e)
        // Something went wrong, display error message.

    Easy, isn't it? Decompression works the same way only that you call ppmd.Uncompress() instead of Compress() and you must used ppmd.GetRatioUncompressed() to get the right ratio.

Final words

Please have a look at the demo application. It's very simple but allows you to test the class. With little effort it's possible to support the compression of several files into one archive, check the orginal code for an example. Some special care must be taken so I advise you to study the code carefully before you do anything.

Compare the compressed file with other programs (BZip, GZip, Rar, Ace, ...) and you will be surprised how well the algorithm works. And it's not too slow! The static library could be changed to support some kind of callback to see how much of the file has been processed yet. Maybe in another version...


This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.

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About the Author

Andreas Muegge
Web Developer
Germany Germany
No Biography provided

Comments and Discussions

QuestionQuestion about PPMd Pin
Member 103249511-Jun-15 3:21
MemberMember 103249511-Jun-15 3:21 
QuestionThe actual ppm algorithm Pin
Sai Hemanth SV22-Mar-12 20:59
MemberSai Hemanth SV22-Mar-12 20:59 
Generalarithmetic code Pin
july ryanhar12-Jul-10 21:11
Memberjuly ryanhar12-Jul-10 21:11 
QuestionWhat about Dmitry Shkarin's PPMD_J compression for non-stationary sources / files? Pin
romulus4-Mar-08 11:52
Memberromulus4-Mar-08 11:52 
Generalarithmetic coding Pin
Ahmed jamil Kattan13-Nov-07 7:04
MemberAhmed jamil Kattan13-Nov-07 7:04 
GeneralPiece of Art Pin
Ahmed jamil Kattan8-Nov-07 11:06
MemberAhmed jamil Kattan8-Nov-07 11:06 
GeneralStepwise Algorithum and flowchart Pin
desaleritesh5-Nov-07 7:37
Memberdesaleritesh5-Nov-07 7:37 
GeneralRe: Stepwise Algorithum and flowchart Pin
Andreas Muegge8-Nov-07 22:08
MemberAndreas Muegge8-Nov-07 22:08 
Generalwhy not cryptography Pin
vishti16-Mar-07 20:18
Membervishti16-Mar-07 20:18 
GeneralRe: why not cryptography Pin
Andreas Muegge21-Mar-07 4:22
MemberAndreas Muegge21-Mar-07 4:22 
Generalwarning while linking demo project Pin
Ozge Colak4-Dec-06 23:26
MemberOzge Colak4-Dec-06 23:26 
Questionhow to choose the best order and subAllocatorSize? [modified] Pin
Ozge Colak15-Jun-06 23:12
MemberOzge Colak15-Jun-06 23:12 
AnswerRe: how to choose the best order and subAllocatorSize? Pin
Andreas Muegge20-Jun-06 0:33
MemberAndreas Muegge20-Jun-06 0:33 
GeneralRe: how to choose the best order and subAllocatorSize? Pin
Ozge Colak20-Jun-06 6:25
MemberOzge Colak20-Jun-06 6:25 
GeneralClarification Pin
Sharmila.manoharan16-Jun-05 21:17
MemberSharmila.manoharan16-Jun-05 21:17 
GeneralRe: Clarification Pin
Andreas Muegge22-Jun-05 21:24
MemberAndreas Muegge22-Jun-05 21:24 
GeneralRe: Clarification Pin
Sharmila.manoharan22-Jun-05 21:35
MemberSharmila.manoharan22-Jun-05 21:35 
GeneralSometimes it's better than ZIP or RAR, but... Pin
andystone28-Apr-05 16:19
Memberandystone28-Apr-05 16:19 
GeneralRe: Sometimes it's better than ZIP or RAR, but... Pin
Andreas Muegge28-Apr-05 21:35
MemberAndreas Muegge28-Apr-05 21:35 
GeneralRe: Sometimes it's better than ZIP or RAR, but... Pin
andystone29-Apr-05 0:28
Memberandystone29-Apr-05 0:28 
GeneralBuffer Compressing (Suggestion) Pin
J. A. Acosta21-Apr-05 11:47
MemberJ. A. Acosta21-Apr-05 11:47 
GeneralRe: Buffer Compressing (Suggestion) Pin
Andreas Muegge21-Apr-05 22:31
MemberAndreas Muegge21-Apr-05 22:31 
GeneralRe: Buffer Compressing (Suggestion) Pin
Ozge Colak12-Jun-06 23:29
MemberOzge Colak12-Jun-06 23:29 
Generalplease help me Pin
hany mohamed mahmoud ibrahim2-Jul-04 15:29
Memberhany mohamed mahmoud ibrahim2-Jul-04 15:29 
GeneralProblem linking in VC++.NET 2003 Pin
paindivine7518-Feb-04 4:58
Memberpaindivine7518-Feb-04 4:58 

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