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.

Date Published: 4 September 2009
PDF: 11 pages
Proc. SPIE 7446, Wavelets XIII, 74460P (4 September 2009); doi: 10.1117/12.826282

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)