In this paper, we present new ways of describing and constructing linear tail-biting trellises for block codes. We extend the well-known Bahl–Cocke–Jelinek–Raviv (BCJR) construction for conventional trellises to tail-biting trellises. The BCJR-like labeling scheme yields a simple specification for the tail-biting trellis for the dual code, with the dual trellis having the same state-complexity profile as that of the primal code . Finally, we show that the algebraic specification of Forney for state spaces of conventional trellises has a natural extension to tail-biting trellises.
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