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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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2009
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/82642 |
| Aporte de: |
| Sumario: | 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. |
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