Results on minimal tail-biting trellis representation of double-circulant wavelet codes

Recently we introduced a new framework to study error control coding using finite-field wavelets. In this paper we show that any double-circulant code over an arbitrary finite-field can be constructed by a simple two-band filter bank structure. Additionally for all double-circulant wavelet codes we introduce efficient tail-biting trellises on which we can perform soft-decision decoding. These tail-biting trellises are called π-minimal in which the product of all state space sizes is minimized.