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We introduce the $q$-potential as an extension of the Benedetto-Fickus frame potential, defined on general reconstruction systems and we 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 Klyachkos and Fultons theory on sums of hermitian operators.
This paper considers the transmission of an infinite sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. While the capac
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $mathcal F$ we describe the spectral and geometrical structure of optimal completions of $mathcal F$ by a finite family of vectors with prescribed norms,
We present an extension of some results of higher order calculus of variations and optimal control to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonl
The noisy broadcast model was first studied in [Gallager, TranInf88] where an $n$-character input is distributed among $n$ processors, so that each processor receives one input bit. Computation proceeds in rounds, where in each round each processor b
Erasure codes are increasingly being studied in the context of implementing atomic memory objects in large scale asynchronous distributed storage systems. When compared with the traditional replication based schemes, erasure codes have the potential