Compensation of Coefficient Erasures in Frame Representations

This work explores low complexity systems to compensate for coefficient erasures in frame representations of signals. Assuming linear synthesis with a pre-specified frame it is demonstrated that erasures can be compensated for even if the origin of the representation coefficients is not known. If the transmitter is aware of the erasure occurrence, the compensation is performed by projecting the erasure error to the remaining coefficients. Furthermore, it is demonstrated that the same compensation can be executed using a transmitter/receiver combination in which the transmitter is not aware of the erasure occurrence. The transmitter compensates for all the coefficients using projections, assuming an erasure will occur. The receiver undoes the compensation for the coefficients that have not been erased, thus maintaining the compensation only of the erased coefficients