Information theoretic bounds for tensor rank minimization over finite fields

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of noiseless and noisy low- rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that reconstruction is based on a rank minimization framework. The derived results show that the smallest number of measurements needed for exact reconstruction is upper bounded by the product of the rank, the order, and the dimension of a cubic tensor. Furthermore, this condition is also sufficient for unique minimization. Similar bounds hold for the noisy rank minimization scenario, except for a scaling function that depends on the channel error probability.

Original languageEnglish (US)
Title of host publication2011 IEEE Global Telecommunications Conference, GLOBECOM 2011
DOIs
StatePublished - Dec 1 2011
Event54th Annual IEEE Global Telecommunications Conference: "Energizing Global Communications", GLOBECOM 2011 - Houston, TX, United States
Duration: Dec 5 2011Dec 9 2011

Publication series

NameGLOBECOM - IEEE Global Telecommunications Conference

Other

Other54th Annual IEEE Global Telecommunications Conference: "Energizing Global Communications", GLOBECOM 2011
CountryUnited States
CityHouston, TX
Period12/5/1112/9/11

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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  • Cite this

    Emad, A., & Milenkovic, O. (2011). Information theoretic bounds for tensor rank minimization over finite fields. In 2011 IEEE Global Telecommunications Conference, GLOBECOM 2011 [6133547] (GLOBECOM - IEEE Global Telecommunications Conference). https://doi.org/10.1109/GLOCOM.2011.6133547