Block error correcting codes using finite-field wavelet transforms

This paper extends the popular wavelet framework for signal representation to error control coding. The primary goal of the paper is to use cyclic finite-field wavelets and filter banks to study arbitrary-rate L-circulant codes. It is shown that the wavelet representation leads to an efficient implementation of the block code encoder and the syndrome generator. A formulation is then given for constructing maximum-distance separable (MDS) wavelet codes using frequency-domain constraints. This paper also studies the possibility of finding a wavelet code whose tail-biting trellis is efficient for soft-decision decoding. The wavelet method may provide an easy way to look for such codes.