A Simple Proof of the Entropy-Power Inequality via Properties of Mutual Information
<|reference_start|>A Simple Proof of the Entropy-Power Inequality via Properties of Mutual Information: While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the EPI hinge on integral representations of differential entropy using either Fisher's information (FI) or minimum mean-square error (MMSE). In this paper, we first present a unified view of proofs via FI and MMSE, showing that they are essentially dual versions of the same proof, and then fill the gap by providing a new, simple proof of the EPI, which is solely based on the properties of mutual information and sidesteps both FI or MMSE representations.<|reference_end|>
@article{rioul2007a,
    title={A Simple Proof of the Entropy-Power Inequality via Properties of Mutual
  Information},
    author={Olivier Rioul},
    journal={arXiv preprint arXiv:cs/0701050},
    year={2007},
    doi={10.1109/ISIT.2007.4557202},
    archivePrefix={arXiv},
    eprint={cs/0701050},
    primaryClass={cs.IT math.IT}
}