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https://github.com/affeldt-aist/infotheo
A Coq formalization of information theory and linear error-correcting codes
https://github.com/affeldt-aist/infotheo
convexity error-correcting-codes information-theory math-comp mathcomp probability ssreflect
Last synced: 8 days ago
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A Coq formalization of information theory and linear error-correcting codes
- Host: GitHub
- URL: https://github.com/affeldt-aist/infotheo
- Owner: affeldt-aist
- License: lgpl-2.1
- Created: 2017-12-20T23:51:11.000Z (almost 7 years ago)
- Default Branch: master
- Last Pushed: 2024-05-23T02:09:20.000Z (5 months ago)
- Last Synced: 2024-05-23T02:28:46.430Z (5 months ago)
- Topics: convexity, error-correcting-codes, information-theory, math-comp, mathcomp, probability, ssreflect
- Language: Coq
- Homepage:
- Size: 3.69 MB
- Stars: 61
- Watchers: 5
- Forks: 14
- Open Issues: 10
-
Metadata Files:
- Readme: README.md
- Changelog: changelog.txt
- License: LICENSE
Awesome Lists containing this project
README
# A Coq formalization of information theory and linear error correcting codes
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Infotheo is a Coq library for reasoning about discrete probabilities,
information theory, and linear error-correcting codes.
## Meta
- Author(s):
- Reynald Affeldt, AIST (initial)
- Manabu Hagiwara, Chiba U. (previously AIST) (initial)
- Jonas Senizergues, ENS Cachan (internship at AIST) (initial)
- Jacques Garrigue, Nagoya U.
- Kazuhiko Sakaguchi, Tsukuba U.
- Taku Asai, Nagoya U. (M2)
- Takafumi Saikawa, Nagoya U.
- Naruomi Obata, Titech (M2)
- Alessandro Bruni, IT-University of Copenhagen
- License: [LGPL-2.1-or-later](LICENSE)
- Compatible Coq versions: Coq 8.18--8.19
- Additional dependencies:
- [MathComp ssreflect](https://math-comp.github.io)
- [MathComp fingroup](https://math-comp.github.io)
- [MathComp algebra](https://math-comp.github.io)
- [MathComp solvable](https://math-comp.github.io)
- [MathComp field](https://math-comp.github.io)
- [MathComp analysis](https://github.com/math-comp/analysis)
- [Hierarchy Builder](https://github.com/math-comp/hierarchy-builder)
- MathComp algebra tactics
- A Coq tactic for proving bounds
- Coq namespace: `infotheo`
- Related publication(s):
- [Robust Mean Estimation by All Means (short paper)]()
- [Trimming Data Sets: a Verified Algorithm for Robust Mean Estimation](https://dl.acm.org/doi/abs/10.1145/3479394.3479412) doi:[10.1145/3479394.3479412](https://doi.org/10.1145/3479394.3479412)
- [Formal Adventures in Convex and Conical Spaces](https://arxiv.org/abs/2004.12713) doi:[10.1007/978-3-030-53518-6_2](https://doi.org/10.1007/978-3-030-53518-6_2)
- [A Library for Formalization of Linear Error-Correcting Codes](https://link.springer.com/article/10.1007/s10817-019-09538-8) doi:[10.1007/s10817-019-09538-8](https://doi.org/10.1007/s10817-019-09538-8)
- [Reasoning with Conditional Probabilities and Joint Distributions in Coq](https://www.jstage.jst.go.jp/article/jssst/37/3/37_3_79/_article/-char/en) doi:[10.11309/jssst.37.3_79](https://doi.org/10.11309/jssst.37.3_79)
- [Examples of formal proofs about data compression](http://staff.aist.go.jp/reynald.affeldt/documents/compression-isita2018.pdf) doi:[10.23919/ISITA.2018.8664276](https://doi.org/10.23919/ISITA.2018.8664276)
- [Formalization of Reed-Solomon codes and progress report on formalization of LDPC codes](http://staff.aist.go.jp/reynald.affeldt/documents/rs_isita2016_author_version.pdf)
- [Formalization of error-correcting codes---from Hamming to modern coding theory](http://staff.aist.go.jp/reynald.affeldt/documents/eccITP2015_authorsversion.pdf) doi:[10.1007/978-3-319-22102-1_2](https://doi.org/10.1007/978-3-319-22102-1_2)
- [Formalization of Shannon’s Theorems](https://link.springer.com/article/10.1007%2Fs10817-013-9298-1) doi:[10.1007/s10817-013-9298-1](https://doi.org/10.1007/s10817-013-9298-1)
## Building and installation instructions
The easiest way to install the latest released version of A Coq formalization of information theory and linear error correcting codes
is via [OPAM](https://opam.ocaml.org/doc/Install.html):
```shell
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-infotheo
```
To instead build and install manually, do (using GNU `make`):
``` shell
git clone https://github.com/affeldt-aist/infotheo.git
cd infotheo
make # or make -j
make -C extraction tests
make install
```
## Acknowledgments
Many thanks to several [contributors](https://github.com/affeldt-aist/infotheo/graphs/contributors).
The principle of inclusion-exclusion is a contribution by
Erik Martin-Dorel (University Toulouse III Paul Sabatier, IRIT research laboratory)
(main theorem: Pr_bigcup_incl_excl; commit 956096859ed89325b2bb74033690ac882bbcd64e)
The variable-length source coding theorems are a contribution by
Ryosuke Obi (Chiba U. (M2))
(commit a67da5e24eaaabb345d225a5bd0f5e86d35413a8)
(with Manabu Hagiwara and Mitsuharu Yamamoto)
Commit 64814f529c1819684c4b8060d0779c24c6339041 was originally by Karl Palmskog
The formalization of modern coding theory is a collaboration with
K. Kasai, S. Kuzuoka, R. Obi
Y. Takahashi collaborated to the formalization of linear error-correcting codes
This work was partially supported by a JSPS Grant-in-Aid for Scientific
Research (Project Number: 25289118), a JSPS Grand-in-Aid for Scientific Research (Project Number: 18H03204)
## Documentation
Each file is documented in its header.
Changes are (lightly) documented in [changelog.txt](changelog.txt).
## Installation with Windows 10 & 11
Installation of infotheo on Windows is less simple.
See [this page](https://github.com/affeldt-aist/mathcomp-install/blob/master/install-windows-en.org)
for instructions to install MathComp on Windows 10 & 11
(or [this page](https://staff.aist.go.jp/reynald.affeldt/ssrcoq/install.html) for instructions in Japanese).
Once MathComp is installed (with opam), do
`opam install coq-infotheo` or `git clone [email protected]:affeldt-aist/infotheo.git; opam install .`
## Original License
Before version 0.2, infotheo was distributed under the terms of the
`GPL-3.0-or-later` license.