Stable interpolation and error correction: concatenated real-codes with an interleaver

We propose a preprocessing technique which allows stable interpolation and error correction. It can be regarded as a parallel concatenated (real) code with an interleaver. We discuss the relative performance and stability of the technique, when compared to the single-channel case (bandlimited interpolation, extrapolation, and error-correction). We give examples that show that the condition numbers of the linear operators involved can be smaller by many orders of magnitude, when compared to the usual bandlimited reconstruction. The stability problem can be formulated using the language of frames. Algorithms for recovering unknown samples (erasures) and for correcting errors at unknown locations are briefly discussed and demonstrated.