Erasure-proof coding with fusion frames

Bernhard G. Bodmann (1) , Gitta Kutyniok (2) , Ali Pezeshki (3)

1 Department of Mathematics, University of Houston
2 Institute of Mathematics, University Osnabrueck
3 Department of Electrical and Computer Engineering [Fort Collins]

The main goal of this paper is the design of frames for transmitting vectors through a memoryless analog erasure channel. The channel transmits the frame coefficients perfectly or discards them, depending on the outcomes of Bernoulli trials with a failure probability q. For sufficiently small q, we construct frames which encode above a fixed non-zero rate and allow the receiver to recover part of the erased coefficients so that the remaining mean-square error vanishes as the frame size increases. We give examples for which the mean-square reconstruction error remaining after corrections are applied decays faster than any inverse power of the number of frame vectors.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Bernhard G. Bodmann, Gitta Kutyniok, Ali Pezeshki. Erasure-proof coding with fusion frames. SAMPTA'09, May 2009, Marseille, France. Special Session on Sampling and Communication. ⟨hal-00451445⟩