Encoder and Distance Properties of Woven Convolutional Codes with One Tailbiting Component Code

Abstract

Woven convolutional codes with one tailbiting component code are studied and their generator matrices are given. It is shown that, if the constituent encoders are identical, a woven convolutional encoder with an outer convolutional warp and one inner tailbiting encoder (WIT) generates the same code as a woven convolutional encoder with one outer tailbiting encoder and an inner convolutional warp (WOT). However, for rate Rtb < 1 tailbiting encoders, the WOT cannot be an encoder realization with a minimum number of delay elements. Lower bounds on the free distance and active distances of woven convolutional codes with a tailbiting component code are given. These bounds are equal to those for woven codes consisting exclusively of unterminated convolutional codes. However, for woven convolutional codes with one tailbiting component code, the conditions for the bounds to hold are less strict.