Wavelet packets for error control coding

Abstract

This paper introduces a class of wavelet packets based upon a set of biorthogonal basis functions. Using a Kronecker product formulation, we develop a self-similar factorization that obeys a set of perfect reconstruction conditions. This construction is then identified as a wavelet packet decomposition and is applied to the finite field case. Finally, it is demonstrated that the proposed wavelet packets can be applied as a well-known class of error control codes.