Error Correction for Erasures of Quantized Frame Coefficients

Bernhard G. Bodmann (1) , Peter G. Casazza (2) , Gitta Kutyniok (3) , Steven Senger (2)

1 Department of Mathematics, University of Houston
2 Department of Mathematics, University of Missouri
3 Institute of Mathematics, University Osnabrueck

In this paper we investigate an algorithm for the suppression of errors caused by quantization of frame coefficients and by erasures in their subsequent transmission. The erasures are assumed to happen independently, modeled by a Bernoulli experiment. The algorithm for error correction in this study embeds check bits in the quantization of frame coefficients, causing a possible, but controlled quantizer overload. If a single-bit quantizer is used in conjunction with codes which satisfy the Gilbert Varshamov bound, then the contributions from erasures and quantization to the reconstruction error is shown to have bounds with the same asymptotics in the limit of large numbers of frame vectors.

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

Bernhard G. Bodmann, Peter G. Casazza, Gitta Kutyniok, Steven Senger. Error Correction for Erasures of Quantized Frame Coefficients. SAMPTA'09, May 2009, Marseille, France. Special Session on frame theory and oversampling. ⟨hal-00451608⟩