Filter bank frame expansions as joint source-channel codes for robustness to erasures

This paper studies oversampled filter banks (OFBs) for robust transmission of multimedia signals over erasure channels. OFBs implement frame expansions, which is an overcomplete expansion of the signal. The 2-channel orthonormal OFB provides a representation of the signal using two orthonormal basis functions. In the event of erasures, conditions under which it is possible to reconstruct the erased values from the received data are studied. This study paves way for message reconstruction in the presence of erasures and quantization noise. Conditions for recovery from some typical erasure patterns like bursty erasures are obtained. We prove that it is not possible to obtain perfect reconstruction if a burst of consecutive erasures of length more than 2 times the filter length occurs.