CMIX

cmix is a lossless data compression program aimed at optimizing compression ratio at the cost of high CPU/memory usage. It gets state of the art results on several compression benchmarks. cmix is free software distributed under the GNU General Public License.

cmix works in Linux, Windows, and Mac OS X. At least 32GB of RAM is recommended to run cmix. Feel free to contact me at byron@byronknoll.com if you have any questions.

GitHub repository: https://github.com/byronknoll/cmix

Downloads

Source Code Release Date Windows Executable
cmix-v17.zip March 24, 2019 cmix-v17-windows.zip
cmix-v16.zip October 3, 2018 cmix-v16-windows.zip
cmix-v15.zip May 5, 2018 cmix-v15-windows.zip
cmix-v14.zip October 20, 2017 cmix-v14-windows.zip
cmix-v13.zip April 24, 2017 cmix-v13-windows.zip
cmix-v12.zip November 7, 2016 cmix-v12-windows.zip
cmix-v11.zip July 3, 2016 cmix-v11-windows.zip
cmix-v10.zip May 30, 2016 cmix-v10-windows.zip
cmix-v9.zip April 8, 2016 cmix-v9-windows.zip
cmix-v8.zip November 10, 2015
cmix-v7.zip February 4, 2015
cmix-v6.zip September 2, 2014
cmix-v5.zip August 13, 2014
cmix-v4.zip July 23, 2014
cmix-v3.zip June 27, 2014
cmix-v2.zip May 29, 2014
cmix-v1.zip April 13, 2014

Benchmarks

Corpus Original size
(bytes)
Compressed size
(bytes)
Compression time
(seconds)
Memory usage
(KiB)
calgary.tar 3152896 539838 2445.52 22449196
silesia 211938580 28632023
enwik6 1000000 176411 688.51 20268624
enwik8 100000000 14877373 60665.32 23039412
enwik9 1000000000 116394271 641189.03 25258492

Compression and decompression time are symmetric. The compressed size can vary slightly depending on the compiler settings used to build the executable.

External Benchmarks

Silesia Open Source Compression Benchmark

File Original size
(bytes)
Compressed size
(bytes)
dickens 10192446 1815773
mozilla 51220480 6874570
mr 9970564 1835587
nci 33553445 800462
ooffice 6152192 1232038
osdb 10085684 1962723
reymont 6627202 706402
samba 21606400 1622361
sao 7251944 3727341
webster 41458703 4309990
xml 5345280 236874
x-ray 8474240 3507902

Calgary Corpus

File Original size
(bytes)
Compressed size
(bytes)
BIB 111261 17336
BOOK1 768771 174750
BOOK2 610856 106939
GEO 102400 42833
NEWS 377109 77587
OBJ1 21504 7063
OBJ2 246814 40467
PAPER1 53161 10905
PAPER2 82199 17267
PIC 513216 21907
PROGC 39611 8377
PROGL 71646 8990
PROGP 49379 6270
TRANS 93695 10098

Canterbury Corpus

File Original size
(bytes)
Compressed size
(bytes)
alice29.txt 152089 31273
asyoulik.txt 125179 29627
cp.html 24603 4791
fields.c 11150 1958
grammar.lsp 3721 785
kennedy.xls 1029744 8043
lcet10.txt 426754 73857
plrabn12.txt 481861 112790
ptt5 513216 21907
sum 38240 6881
xargs.1 4227 1131

Description

I started working on cmix in December 2013. Most of the ideas I implemented came from the book Data Compression Explained by Matt Mahoney.

cmix uses three main components:

  1. Preprocessing
  2. Model prediction
  3. Context mixing

The preprocessing stage transforms the input data into a form which is more easily compressible. This data is then compressed using a single pass, one bit at a time. cmix generates a probabilistic prediction for each bit and the probability is encoded using arithmetic coding.

cmix uses an ensemble of independent models to predict the probability of each bit in the input stream. The model predictions are combined into a single probability using a context mixing algorithm. The output of the context mixer is refined using an algorithm called secondary symbol estimation (SSE).

Architecture

architecture

Preprocessing

cmix uses a transformation on three types of data:

  1. Binary executables
  2. Natural language text
  3. Images

The preprocessor uses separate components for detecting the type of data and actually doing the transformation.

For images and binary executables, I used code for detection and transformation from the open source paq8pxd program.

I wrote my own code for detecting and transforming natural language text. It uses an English dictionary and a word replacing transform. The dictionary comes from the phda Hutter prize entry and is 415,377 bytes.

As seen on the Silesia benchmark, additional preprocessing using the precomp program can improve cmix compression on some files.

Model Prediction

cmix v17 uses a total of 2,122 independent models. There are a variety of different types of models, some specialized for certain types of data such as text, executables, or images. For each bit of input data, each model outputs a single floating point number, representing the probability that the next bit of data will be a 1. The majority of the models come from other open source compression programs: paq8l, paq8pxd, and paq8hp12any.

LSTM Mixer

architecture

The byte-level mixer uses long short-term memory (LSTM) trained using backpropagation through time. It uses Adam optimization with learning rate decay. The LSTM forget and input gates are coupled. I created another project called lstm-compress which compresses data using only LSTM. lstm-compress results are posted on the Large Text Compression Benchmark.

Context Mixing

mixer

cmix uses a similar neural network architecture to paq8. This architecture is also known as a gated linear network. cmix uses three layers of weights.

Comparison to PAQ8

cmix shares many similarities to the PAQ8 family of compression programs. There are many different branches of PAQ8. Here are some of the major differences between cmix and other PAQ8 variants:

Acknowledgements

Thanks to AI Grant for funding cmix.

cmix uses ideas and source code from many people in the data compression community. Here are some of the major contributors: