Random fusion frames for loss-insensitive packet encoding

Bernhard G. Bodmann; Pankaj K. Singh

doi:10.1117/12.2023353

26 September 2013 Random fusion frames for loss-insensitive packet encoding

Bernhard G. Bodmann, Pankaj K. Singh

Proceedings Volume 8858, Wavelets and Sparsity XV; 88580F (2013) https://doi.org/10.1117/12.2023353
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

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.

Citation Download Citation

Bernhard G. Bodmann and Pankaj K. Singh "Random fusion frames for loss-insensitive packet encoding", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580F (26 September 2013); https://doi.org/10.1117/12.2023353

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