Parity-Check Matrix Calculation for Paraunitary Oversampled DFT Filter Banks

Joint source-channel coding schemes based on oversampled filter banks were recently proposed. Oversampled filter banks are considered as error-correcting codes, extending the notion of code subspace, parity-check matrix, and syndrome to the domain of real and complex numbers. We here present an efficient calculation and implementation of the parity-check polynomial matrices for oversampled discrete Fourier transform (DFT) filter banks. If desired, the calculation of the parity-check polynomials can be performed as part of the prototype filter design procedure. We compare our method to those previously presented in the literature.