CMIX

cmix is a lossless data compression program aimed at optimizing compression ratio at the cost of high CPU/memory usage. cmix is free software distributed under the GNU General Public License.

cmix is currently ranked first place on the Silesia Open Source Compression Benchmark, second place on the Large Text Compression Benchmark and first place on the Lossless Photo Compression Benchmark. It also has state of the art results on the Calgary Corpus and Canterbury Corpus.

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-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 549098 2446.18 20403492
silesia 211938580 29359909
enwik6 1000000 180865 588.41 20060276
enwik8 100000000 15210458 60183.9 25051896
enwik9 1000000000 119017492 627802.1 28287648

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

Silesia Open Source Compression Benchmark

File Original size
(bytes)
Compressed size
(bytes)
dickens 10192446 1849638
mozilla 51220480 7173820
mr 9970564 1906359
nci 33553445 816615
ooffice 6152192 1269599
osdb 10085684 1978118
reymont 6627202 745023
samba 21606400 1659622
sao 7251944 3740293
webster 41458703 4456839
xml 5345280 241960
x-ray 8474240 3522023

Calgary Corpus

File Original size
(bytes)
Compressed size
(bytes)
BIB 111261 17873
BOOK1 768771 177956
BOOK2 610856 109205
GEO 102400 43235
NEWS 377109 79454
OBJ1 21504 7307
OBJ2 246814 41225
PAPER1 53161 11120
PAPER2 82199 17612
PIC 513216 21778
PROGC 39611 8567
PROGL 71646 9243
PROGP 49379 6449
TRANS 93695 10369

Canterbury Corpus

File Original size
(bytes)
Compressed size
(bytes)
alice29.txt 152089 31849
asyoulik.txt 125179 30157
cp.html 24603 4967
fields.c 11150 2032
grammar.lsp 3721 824
kennedy.xls 1029744 8424
lcet10.txt 426754 75286
plrabn12.txt 481861 114379
ptt5 513216 21778
sum 38240 7179
xargs.1 4227 1182

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.

Architecture

architecture

The byte-level mixer uses long short-term memory (LSTM) trained using backpropagation through time. I created another project called lstm-compress which compresses data using only LSTM. The output of the bit-level context mixer is refined using an algorithm called secondary symbol estimation (SSE).

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 natural language text. For transforming the text, I used code from the open source paq8hp12any program. This uses an English dictionary and a word replacing transform. The dictionary is 463,903 bytes.

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

Model Prediction

cmix v14 uses a total of 1,867 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.

Context Mixing

mixer

cmix uses a similar neural network architecture to paq8l. This architecture is also known as a gated linear network. cmix v14 uses three layers of connections, with 415,257 neurons and 768,153,146 weights.

There are some differences compared to standard neural network implementations:

  1. Every neuron in the network directly tries to minimize cross entropy, so there is no backpropagation of gradients between layers.
  2. Only a small subset of neurons are activated for each prediction. The activations are based on a set of contexts (i.e. functions of the recent input history). The context-dependent activations improve prediction and reduce computational complexity.
  3. Instead of using a global learning rate, each context set has its own learning rate parameter.

Acknowledgements

Thanks to AI Grant for funding cmix.

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