Efficient solution of block linear systems with Toeplitz entries using a channel decomposition technique (Q1329429)

The paper is concentrated on the development of efficient solvers for block linear systems with Toeplitz entries. The importance of the problem, considered, is defined by a wide range of applications, which such solvers have in digital signal processing. A novel channel decomposition technique is applied in order to obtain fast procedure for matrices' operations. Two algorithms are proposed which require scalar operations only. The basic algorithm structures are derived. An efficient lattice structure, that requires scalar operations only, is also derived. The results admit full parallelism and they reduce processing time by an order of magnitude. Stressing on the very important case, namely highly concurrent order recursive algorithm, is done. A novel partition strategy, named ``channel decomposition technique'' has been applied to derive two terms recursion that need scalar operations only. Both developed algorithms can be applied to solve the problem that arise in multichannel and multidimensional Wiener filtering, smoothing and prediction. Finally, Matlab code is provided for the algorithms' realisations and applications.