Frames And Erasures

Frames have been useful in signal transmission due to the built in redundancy. In recent years, the erasure problem in data transmission has been the focus of considerable research in the case the error estimate is measured by operator (or matrix) norm. Sample results include the characterization of one-erasure optimal Parseval frames, the connection between two-erasure optimal Parseval frames and equiangular frames, and some characterization of optimal dual frames. If iterations are allowed in the reconstruction process of the signal vector, then spectral radius measurement for the error operators is more appropriate than the operator norm measurement. A complete characterization of spectrally one-uniform frames (i.e., one-erasure optimal frames with respect to the spectral radius measurement) in terms of the redundancy distribution of the frame is obtained. The characterization relies on the connection between spectrally optimal frames and the linear connectivity property of the frame. The linear connectivity property is equivalent to the intersection dependence property, and is also closely related to the concept of k-independent set. © Springer India 2014