Loss-Insensitive Vector Encoding with Two-Uniform Frames

Bernhard G. Bodmann; Vern I. Paulsen

doi:10.1117/12.615773

17 September 2005 Loss-insensitive vector encoding with two-uniform frames

Bernhard G. Bodmann, Vern I. Paulsen

Proceedings Volume 5914, Wavelets XI; 591403 (2005) https://doi.org/10.1117/12.615773
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

The central topic of this paper is the linear, redundant encoding of vectors using frames for the purpose of loss-insensitive data transmission. Our goal is to minimize the reconstruction error when frame coefficients are accidentally erased. Two-uniform frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest Euclidean error norm when up to two frame coefficients are set to zero. Here, we consider the case when an arbitrary number of the frame coefficients of a vector is lost. We derive general error bounds and apply these to concrete examples. We show that among the 227 known equivalence classes of two-uniform (36,15)-frames arising from Hadamard matrices, there are 5 that give smallest error bounds for up to 8 erasures.

Citation Download Citation

Bernhard G. Bodmann and Vern I. Paulsen "Loss-insensitive vector encoding with two-uniform frames", Proc. SPIE 5914, Wavelets XI, 591403 (17 September 2005); https://doi.org/10.1117/12.615773

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