The paper presents two efficient Viterbi decoding-based suboptimal algorithms for tailbiting codes. The first algorithm, the wrap-around Viterbi algorithm (WAVA), falls into the circular decoding category. It processes the tailbiting trellis iteratively, explores the initial state of the transmitted sequence through continuous Viterbi decoding, and improves the decoding decision with iterations. A sufficient condition for the decision to be optimal is derived. For long tailbiting codes, the WAVA gives essentially optimal performance with about one round of Viterbi trial. For short- and medium-length tailbiting codes, simulations show that the WAVA achieves closer-to-optimum performance with fewer decoding stages compared with the other suboptimal circular decoding algorithms. The second algorithm, the bidirectional Viterbi algorithm (BVA), employs two wrap-around Viterbi decoders to process the tailbiting trellis from both ends in opposite directions. The surviving paths from the two decoders are combined to form composite paths once the decoders meet in the middle of the trellis. The composite paths at each stage thereafter serve as candidates for decision update. The bidirectional process improves the error performance and shortens the decoding latency of unidirectional decoding with additional storage and computation requirements. Simulation results show that both proposed algorithms effectively achieve practically optimum performance for tailbiting codes of any length.

This paper presents two simple and effective criteria for stopping the iteration process in turbo decoding with a negligible degradation of the error performance. Both criteria are devised based on the cross-entropy (CE) concept. They are as efficient as the CE criterion, but require much less and simpler computations.