Arbitrary rate maximum-distance separable wavelet codes

This paper expands on the idea of wavelet coding. It undertakes construction of arbitrary rate error correcting codes using finite-field wavelets and filter banks. We show that a rate K / L code can be constructed by a combination of a K-band trivial analysis bank and an L-band synthesis bank. Several issues regarding these wavelet codes are investigated. Among other results, we develop a methodology to construct maximum-distance separable (MDS) codes using finite-field wavelets. In this method, a rate K / L code is constructed by a direct sum of the K rate 1/L subcodes which have been designed using the Bose-Chaudhuri-Hocquenghem (BCH) bound such that their direct sum generates an MDS code.