Spread representations

Abstract

Sparse representations, where one seeks to represent a vector on a redundant basis using the smallest number of basis vectors, appears to have numerous applications. The other extreme, where one seeks a representation that uses all the basis vectors, might be of interest if one manages to spread the information nearly equally over all of them. Minimizing the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm of the vector of weights is one way the find such a representation. Properties of this solution and dedicated fast algorithms allowing to find it are developed. Applications are to be found in robust data coding and improving achievable data rates over amplitude constrained channels.