The modified wrap-around Viterbi algorithm for convolutional tail-biting codes

Recently, two near-optimal decoding algorithms [Shao, R.Y., Lin, S., and Fossorier, M.P.C., 2003. Two decoding algorithms for tailbiting codes. IEEE transactions on communications, 51 (10), 1658-1665; Krishnan, K.M. and Shankar, P., 2006. Approximate linear time ML decoding on tail-biting trellises in two rounds. In IEEE international symposium on information theory, Seattle, WA, USA, pp. 2245-2249] have been proposed for convolutional tail-biting codes. Both algorithms iterate the Viterbi algorithm twice, but use different metrics in the second iteration. Simulations showed that the latter algorithm (Krishnan and Shankar 2006) improved on the earlier one (Shao et al. 2003) in word error rates at the price of additional storage consumption. In this work, we prove that with a proper modification to the earlier one, the two algorithms can be made to have exactly the same survivor path at each state in the trellis, and hence are equivalent in error performance. One can consequently adopt the modified algorithm to alleviate the need for extra storage consumption of the later algorithm and, at the same time, achieve equally good performance.