Termination and tailbiting of rate-k/n direct product convolutional codes

In this paper we extend the algorithms for the termination and tailbiting of direct product convolutional codes, that we proposed in a previous paper, to the rate-k/n case. There, the relationship between the direct product encoder state sequence and the parameters of the vertical and horizontal constituent encoders was derived, and, given a generic information sequence, it was shown how to find the terminating sequence for the direct product encoder of Rate R = 1/n. An algorithm was also proposed for tailbiting rate-1/n direct product convolutional codes. In this paper, we investigate on the tailbiting failure conditions, which were not addressed before, and extend the proposed tailbiting algorithm to the general rate-k/n case.