The objective of this paper is to study the performance of fusion frames for packet encodings in the presence of erasures. These frames encode a vector in a Hilbert space in terms of its components in subspaces, which can be identified with packets of linear coefficients. We evaluate the fusion frame performance under some statistical assumption on the vector to be transmitted, when part of the packets is transmitted perfectly and another part is lost in an adversarial, deterministic manner. The performance is measured by the mean-squared Euclidean norm of the reconstruction error when averaged over the transmission of all unit vectors. Our main result is that a random selection of fusion frames performs nearly as well as previously known optimal bounds for the error, characterized by optimal packings of subspaces, which are known not to exist in all dimensions.

Date Published: 26 September 2013
PDF: 12 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88580F (26 September 2013); doi: 10.1117/12.2023353

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)