Optimal reconstruction systems for erasures and for the q-potential

In this paper we introduce the q-potential as an extension of the Benedetto-Fickus frame potential, defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal...

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Autor principal: Massey, Pedro Gustavo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2009
Materias:
Matemática
Compatible unitarily invariant norm
Erasures
q-Fundamental inequality
q-Potential
Reconstruction systems
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/82642
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-82642
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Compatible unitarily invariant norm
Erasures
q-Fundamental inequality
q-Potential
Reconstruction systems
spellingShingle Matemática
Compatible unitarily invariant norm
Erasures
q-Fundamental inequality
q-Potential
Reconstruction systems
Massey, Pedro Gustavo
Optimal reconstruction systems for erasures and for the q-potential
topic_facet Matemática
Compatible unitarily invariant norm
Erasures
q-Fundamental inequality
q-Potential
Reconstruction systems
description In this paper we introduce the q-potential as an extension of the Benedetto-Fickus frame potential, defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computed with respect to a compatible unitarily invariant norm. We finally describe necessary and sufficient (spectral) conditions, that we call q-fundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko's and Fulton's theory on sums of hermitian operators.
format Articulo
Articulo
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
author_sort Massey, Pedro Gustavo
title Optimal reconstruction systems for erasures and for the q-potential
title_short Optimal reconstruction systems for erasures and for the q-potential
title_full Optimal reconstruction systems for erasures and for the q-potential
title_fullStr Optimal reconstruction systems for erasures and for the q-potential
title_full_unstemmed Optimal reconstruction systems for erasures and for the q-potential
title_sort optimal reconstruction systems for erasures and for the q-potential
publishDate 2009
url http://sedici.unlp.edu.ar/handle/10915/82642
work_keys_str_mv AT masseypedrogustavo optimalreconstructionsystemsforerasuresandfortheqpotential
bdutipo_str Repositorios
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