Oversampled Filter Banks with instantaneous erasures

Oversampled Filter Banks (OFB) can be used for erasure correction due to the redundancy that they insert into the signal. People have studied erasures using a frame-theoretic approach in which erasure is defined as the deletion of the frame expansion coefficients corresponding to a frame element. This approach applies to OFBs and results in an erasure being interpreted as losing all samples in a sub-band. However, a more realistic and flexible scenario is when an erasure is considered as the loss of sub-band samples only for particular time instances. Alternatively in an erasure-free channel, analogous to the concept of puncturing, the sub-band samples might be erased deliberately to change the code rate. In both of these scenarios, the erasure pattern of sub-bands can differ for different time instances. In this paper, we investigate this situation and derive a set of sufficient conditions that should be satisfied by the OFB in order to reconstruct the output. Simulation results will be presented for substantiating the proposed OFB structure which show the efficiency of this method in increasing the resilience of OFB against erasures.