Spectrally Two–Uniform Frames For Erasures

Keywords

Connected frames; Erasures; Frames; K -independent sets; Redundancy distribution; Spectrally optimal dual frames

Abstract

We continue to work on the problem of characterizing erasure-optimal frames when spectral radius is used as a measurement of the error operator. Spectrally optimal (N,n) -frames for one erasures are the ones that the minimal spectral error n/N can be achieved. This class of frames was completely characterized in [28] in terms of the connectivity property and the redundancy distributions of the involved frames. We show that the best spectral error for the two erasures is always greater than or equal to [Formula Presented]. We characterize all the frames such that the above lower bound can be achieved. Different characterizations are also obtained for the case that when N = n+1 or n+2. We show that in these special cases, spectrally 2-erasure optimal frames are related to the n-independence property of frames.

Publication Date

6-1-2015

Publication Title

Operators and Matrices

Volume

9

Issue

2

Number of Pages

383-399

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.7153/oam-09-23

Socpus ID

84929168839 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84929168839

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