Termination and tailbiting of direct product convolutional codes

In this paper we propose some algorithms for the termination and tailbiting of direct product convolutional codes, whose definition was given in a previous paper by M. Bossert, C. Medina, and V. Sidorenko. There, the properties of these codes were investigated analyzing their generator and parity check matrices. We assume to encode these codes by feedback convolutional encoders realized in controller canonical form. The relationship between the direct product encoder state sequence and the parameters of the vertical and horizontal constituent encoders is derived first. Afterwards, given a generic information sequence, it is shown how to find the terminating sequence for the direct product encoder and an algorithm is also proposed for tailbiting, i.e., for finding the encoder starting state such that the encoder, after being fed with the information sequence, ends in the same state where it started from.