Oversampled filter banks as error correcting codes: theory and impulse noise correction

Oversampled filter banks (OFBs) provide an overcomplete representation of their input signal. This paper describes how OFBs can be considered as error-correcting codes acting on real or complex sequences, very much like classical binary convolutional codes act on binary sequences. The structured redundancy introduced by OFBs in subband signals can be used to increase robustness to noise. In this paper, we define the notions of code subspace, syndrome, and parity-check polynomial matrix for OFBs. Furthermore, we derive generic expressions for projection-based decoding, suitable for the case when a simple second-order model completely characterizes the noise incurred by subband signals. We also develop a nonlinear hypotheses-test based decoding algorithm for the case when the noise in subbands is constituted by a Gaussian background noise and impulsive errors (a model that adequately describes the action of both quantization noise and transmission errors). Simulation results show that the algorithm effectively removes the effect of impulsive errors occurring with a probability of 10^-3.