Abstract

A circular MAP decoder for error-correcting trellis codes that employ tail biting produces soft-decision outputs provides an estimate of the probabilities of the states in the first stage of the trellis, which probabilities replace the a priori knowledge of the starting state in a conventional MAP decoder. The circular MAP decoder provides the initial state probability distribution in either of two ways. The first involves a solution to an eigenvalue problem for which the resulting eigenvector is the desired initial state probability distribution; with knowledge of the starting state, the circular MAP decoder performs the rest of the decoding according to the MAP decoding algorithm. The second is based on a recursion for which the iterations converge to a starting state distribution. After sufficient iterations, a state on the circular sequence of states is known with high probability, and the circular MAP decoder performs the rest of the decoding according to the MAP decoding algorithm.

Other References

• L.R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate," IEEE Transactions on Information Theory, pp. 284-287, Mar. 1974
• J.B. Anderson and K. Balachandran, "Decision depths of convolutional codes," IEEE Trans. Information Theory, vol. IT-35, pp. 455-459, Mar. 1989
• R.V. Cox and C-E Sundberg, "An Efficient Adaptive Circular Viterbi Algorithm for Decoding Generalized Tailbiting Convolutional Codes," IEEE Transactions on Vehicular Technology, vol. 43, No. 1, pp. 57-68, Feb. 1994
• H.H. Ma and J.K. Wolf, "On tail biting convolutional codes," IEEE Transactions on Communications, vol. 34, No., pp. 104-111, Feb. 1986
• Q. Wang and V.K. Bhargava, "An efficient maximum likelihood decoding algorithm for generalized tailbiting convolutional codes including quasicyclic codes," IEEE Transactions on Communications, vol. 37, No. 8, pp. 875-879, Aug. 1989
• J.B. Anderson and Seshadri Mohan, "Source and Channel Coding," pp. 216 and 336-34