Erasure-proof transmissions: fusion frames meet coding theory

Bernhard G. Bodmann; Gitta Kutyniok

doi:10.1117/12.826282

4 September 2009 Erasure-proof transmissions: fusion frames meet coding theory

Bernhard G. Bodmann, Gitta Kutyniok

Proceedings Volume 7446, Wavelets XIII; 74460P (2009) https://doi.org/10.1117/12.826282
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

In this paper we analyze the use of frames for the transmission and error-correction of analog signals via a memoryless erasure-channel. We measure performance in terms of the mean-square error remaining after error correction and reconstruction. Our results continue earlier works on frames as codes which were mostly concerned with the smallest number of erased coefficients. To extend these works we borrow some ideas from binary coding theory and realize them with a novel class of frames, which carry a particular fusion frame architecture. We show that a family of frames from this class achieves a mean-square reconstruction error remaining after corrections which decays faster than any inverse power in the number of frame coefficients.

Citation Download Citation

Bernhard G. Bodmann and Gitta Kutyniok "Erasure-proof transmissions: fusion frames meet coding theory", Proc. SPIE 7446, Wavelets XIII, 74460P (4 September 2009); https://doi.org/10.1117/12.826282

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