Publications by Emmanuel Abbé

Chaining Mutual Information and Tightening Generalization Bounds

Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the h ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Polarization of the Renyi Information Dimension With Applications to Compressed Sensing

Emmanuel Abbé, Saeid Haghighatshoar

In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi Information Dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we prove that the R ...

Ieee-Inst Electrical Electronics Engineers Inc2017

Polar Codes for Broadcast Channels

Michael Christoph Gastpar, Emmanuel Abbé, Naveen Goela

Polar codes are introduced for discrete memoryless broadcast channels. For m-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from m-independent messages to one codeword while satisfying broadcast constrai ...

Institute of Electrical and Electronics Engineers2015

A New Entropy Power Inequality for Integer-Valued Random Variables

Emmanuel Abbé, Saeid Haghighatshoar

The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for spe ...

Institute of Electrical and Electronics Engineers2014

Polar Codes For Broadcast Channels

Michael Christoph Gastpar, Emmanuel Abbé, Naveen Goela

Building on polar code constructions proposed by the authors for deterministic broadcast channels, two theorems are introduced in the present paper for noisy two-user broadcast channels. The theorems establish polar code constructions for two important ...

2013

Proof of the Outage Probability Conjecture for MISO Channels

Emre Telatar, Emmanuel Abbé

It is conjectured that the covariance matrices minimizing the outage probability under a power constraint for multiple-input multiple-output channels with Gaussian fading are diagonal with either zeros or constant values on the diagonal. In the multiple-in ...

Institute of Electrical and Electronics Engineers2013

Polar Codes for the m-User MAC

Emre Telatar, Emmanuel Abbé

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arıkan’s polarization technique applied individually to each user transforms independent uses of a m-user binary input MAC into suc ...

Institute of Electrical and Electronics Engineers2012

A coordinate system for Gaussian Networks

Emmanuel Abbé

This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown that in these pr ...

Institute of Electrical and Electronics Engineers2012

Adaptive sensing using deterministic partial Hadamard matrices

Emre Telatar, Emmanuel Abbé, Saeid Haghighatshoar

This paper investigates the construction of determin- istic measurement matrices preserving the entropy of a random vector with a given probability distribution. In particular, it is shown that for a random vector with i.i.d. discrete components, this is a ...

Ieee2012

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Emmanuel Abbé

Entropic Matroids and Their Representation

Chaining Mutual Information and Tightening Generalization Bounds

Polarization of the Renyi Information Dimension With Applications to Compressed Sensing

Polar Codes for Broadcast Channels

A New Entropy Power Inequality for Integer-Valued Random Variables

Polar Codes For Broadcast Channels

Proof of the Outage Probability Conjecture for MISO Channels

Polar Codes for the m-User MAC

A coordinate system for Gaussian Networks

Adaptive sensing using deterministic partial Hadamard matrices

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Entropic Matroids and Their Representation

A New Entropy Power Inequality for Integer-Valued Random Variables

Polar Codes for Broadcast Channels

Chaining Mutual Information and Tightening Generalization Bounds

Proof of the Outage Probability Conjecture for MISO Channels

Polar Codes for the m-User MAC

A coordinate system for Gaussian Networks

Polarization of the Renyi Information Dimension With Applications to Compressed Sensing

Adaptive sensing using deterministic partial Hadamard matrices

Polar Codes For Broadcast Channels