Set of Joint Distributions Achieving Positive Zero-Outage Capacities

This repository contains supplementary material for the papers "On the Set of Joint Rayleigh Fading Distributions Achieving Positive Zero-Outage Capacities" (Karl-L. Besser, Pin-Hsun Lin, and Eduard Jorswieck, 2020 54th Asilomar Conference on Signals, Systems, and Computers, Nov. 2020, doi:10.1109/IEEECONF51394.2020.9443271) and "On Fading Channel Dependency Structures with a Positive Zero-Outage Capacity" (Karl-L. Besser, Pin-Hsun Lin, and Eduard Jorswieck, IEEE Transactions to Communications, vol. 69, no. 10, pp. 6561-6574, Oct. 2021, doi:10.1109/TCOMM.2021.3097755, arXiv:2102.02541).

The files specific to the conference version can be found in the asilomar2020 branch.

The idea is to give an interactive version of the calculations and presented concepts to the reader. One can also change different parameters and explore different behaviors on their own.

File List

The following files are provided in this repository:

Maximum Ratio Combining.ipynb: Jupyter notebook that contains the MRC examples.
Selection Combining.ipynb: Jupyter notebook that contains the SC examples.
Example - Clayton Copula.ipynb: Jupyter notebook that illustrates an example of a positive ZOC with an underlying Clayton copula.
rayleigh_fading.py: Python module that contains the calculations of the ZOC for Rayleigh fading channels.
nakagami_fading.py: Python module that contains the calculations of the ZOC for Nakagami-m fading channels.
maximum_ratio_combining.py: Python module that contains the calculations of the MRC examples.
selection_combining.py: Python module that contains the calculations of the SC examples.
boundary.py: Python module that contains an illustration of the ZOC idea (boundary of the support).
copulas.py: Python module that contains the copulas used to construct joint distributions with positive ZOCs.
utils.py: Python module that contains some helper functions

Usage

Running it online

The easiest way is to use services like Binder to run the notebook online. Simply navigate to https://mybinder.org/v2/gl/klb2%2Fzero-outage-joint-distributions/master to run the notebooks in your browser without setting everything up locally.

Local Installation

If you want to run it locally on your machine, Python3 and Jupyter are needed. The present code was developed and tested with the following versions:

Python 3.8
Jupyter 1.0
numpy 1.18
scipy 1.4

Make sure you have Python3 installed on your computer. You can then install the required packages (including Jupyter) by running

pip3 install -r requirements.txt
jupyter nbextension enable --py widgetsnbextension

This will install all the needed packages which are listed in the requirements file. The second line enables the interactive controls in the Jupyter notebooks.

Finally, you can run the Jupyter notebooks with

jupyter notebook 'Maximum Ratio Combining.ipynb'

You can also recreate the figures from the paper by running

bash run.sh

Acknowledgements

This research was supported in part by the Deutsche Forschungsgemeinschaft (DFG) under grant JO 801/23-1.

License and Referencing

This program is licensed under the GPLv3 license. If you in any way use this code for research that results in publications, please cite our original article listed above.

You can use the following BibTeX entry

@article{Besser2021zoc,
	author = {Besser, Karl-Ludwig and Lin, Pin-Hsun and Jorswieck, Eduard A.},
	title = {On Fading Channel Dependency Structures with a Positive Zero-Outage Capacity},
	journal = {{IEEE} Transactions on Communications},
	year = {2021},
	volume = {69},
	number = {10},
	month = {10},
	pages = {6561--6574},
	eprint = {2102.02541},
	archivePrefix = {arXiv},
	primaryClass = {cs.IT},
	doi = {10.1109/TCOMM.2021.3097755},
}