DeepAI AI Chat

Delocalisation of one-dimensional marginals of product measures and the capacity of LTI discrete channels

09/03/2018

∙

by Maxime Bombar, et al.

∙

The University of Sydney

∙

∙

We consider discrete linear time invariant (LTI) channels satisfying the phase independence (PI) assumption. We show that under the PI assumption the capacity of LTI channels is positive. The main technical tool that we use to establish the positivity of the capacity is the delocalisation theorem for one-dimensional marginals of the product measure due to Ball and Nazarov. We also prove two delocalisation results that can be seen as extensions of Ball-Nazarov Theorem.

Maxime Bombar
4 publications
Alexander Fish
1 publication

∙ 11/10/2019

On the Capacity of Channels with Deletions and States

We consider the class of channels formed from the concatenation of a del...

0 Yonglong Li, et al. ∙

∙ 04/09/2019

New Converse Bounds for Discrete Memoryless Channels in the Finite Blocklength Regime

We study the determination problem of the channel capacity for the discr...

0 Yasutada Oohama, et al. ∙

∙ 01/09/2019

A Deterministic Algorithm for the Capacity of Finite-State Channels

We propose a modified version of the classical gradient descent method t...

0 Chengyu Wu, et al. ∙

∙ 10/31/2021

Capacity of Noisy Permutation Channels

We establish the capacity of a class of communication channels introduce...

0 Jennifer Tang, et al. ∙

∙ 02/04/2021

Formalized Haar Measure

We describe the formalization of the existence and uniqueness of Haar me...

0 Floris van Doorn, et al. ∙

∙ 08/30/2018

Capacity of Locally Recoverable Codes

Motivated by applications in distributed storage, the notion of a locall...

0 Arya Mazumdar, et al. ∙

∙ 02/24/2021

It was "all" for "nothing": sharp phase transitions for noiseless discrete channels

We establish a phase transition known as the "all-or-nothing" phenomenon...

0 Jonathan Niles-Weed, et al. ∙