Suboptimum MAP–Decoding of Tail–Biting Codes Using the Dual Trellis

Christian Weiß and Jens Berkmann Institute for Communications Engineering (LNT) Munich University of Technology (TUM) e-mail: Christian.Weiss,Jens.Berkmann @ei.tum.de The trellis of a finite abelian group code is locally (i.e., trellis section by trellis section) related to the trellis of the corresponding dual group code. This allows to express the update rules of the BCJR algorithm operating on a single trellis section of the primal trellis in terms of the corresponding dual trellis section. Using this local approach any (essentially) section–based BCJR–like algorithm can be dualized. Given this, the well-known complexity advantage of the dual approach for high–rate codes can be generalized from the class of exact MAP algorithms to the broader class of suboptimum MAP algorithms which may be more attractive for practical applications because of their reduced complexity. As an example we give the dual implementation of a suboptimal MAP decoding algorithm for tail–biting convolutional codes. I. PRELIMINARIES A. Notations and Definitions We assume a finite lengthtime axis , a symbol space "!$#&%('*) # being the Cartesian product of finite abelian symbol groups ) # ,+.-/ , and a code 0213 being a subgroup of the symbol space with component–wise group operation. Each symbol group