A View of Information-Estimation Relations in Gaussian Networks

Séminaire le 9 Octobre 2017, 14h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Prof. Shlomo Shamai (Andrew and Erna Viterbi Department of Electrical Engineering)

This talk will focus on the recent applications of Information-Estimation Relations to Gaussian Networks. In the first part of the talk, we will go over recent connections between estimation theoretic and information theoretic measures. The estimation theoretic measures that would
be of importance to us are the Minimum Means p-th Error (MMPE) and its special case the Minimum Mean Square Error (MMSE). As will be demonstrated, the MMSE can be very useful in bounding mutual information via the I-MMSE relationship of Guo-Shamai-Verdu, and the MMPE can be used to bound the conditional entropy via the moment entropy inequality. In the second part of the talk, we will discuss several applications of Information-Estimation Relations in Gaussian noise networks. As the first application, we show how the I-MMSE relationship can be used to determine the behavior, for every signal-to-noise ratio (SNR), of the mutual information and the MMSE of the transmitted codeword for the setting of the Gaussian Broadcast Channel and the Gaussian Wiretap Channel. As a second application, the notion of the MMPE is used to generalize the Ozarow-Wyner lower bound on the mutual information for discrete inputs on Gaussian noise channels. A short outlook of future applications concludes the presentation.

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This work is in collaboration with R. Bustin, A. Dytso, H. Vincent Poor, Daniela Tuninetti, Natasha Devroye, and it is supported by the European Union's Horizon 2020 Research And Innovation Programme, grant agreement no. 694630.