Controlled Loosening-up (CLuP) – achieving exact MIMO ML in polynomial time

by   Mihailo Stojnic, et al.

In this paper we attack one of the most fundamental signal processing/informaton theory problems, widely known as the MIMO ML-detection. We introduce a powerful Random Duality Theory (RDT) mechanism that we refer to as the Controlled Loosening-up (CLuP) as a way of achieving the exact ML-performance in MIMO systems in polynomial time. We first outline the general strategy and then discuss the rationale behind the entire concept. A solid collection of results obtained through numerical experiments is presented as well and found to be in an excellent agreement with what the theory predicts. As this is the introductory paper of a massively general concept that we have developed, we mainly focus on keeping things as simple as possible and put the emphasis on the most fundamental ideas. In our several companion papers we present various other complementary results that relate to both, theoretical and practical aspects and their connections to a large collection of other problems and results that we have achieved over the years in Random Duality.


page 1

page 2

page 3

page 4


Complexity analysis of the Controlled Loosening-up (CLuP) algorithm

In our companion paper <cit.> we introduced a powerful mechanism that we...

Rephased CLuP

In <cit.> we introduced CLuP, a Random Duality Theory (RDT) based algori...

Starting CLuP with polytope relaxation

The Controlled Loosening-up (CLuP) mechanism that we recently introduced...

Sparse linear regression – CLuP achieves the ideal exact ML

In this paper we revisit one of the classical statistical problems, the ...

Algorithmic random duality theory – large scale CLuP

Based on our Random Duality Theory (RDT), in a sequence of our recent pa...

Polynomial and trigonometric splines

Classes of simple polynomial and simple trigonometric splines given by F...

Contractility of continuous optimization

By introducing the concept of contractility, all the possible continuous...