Further results on unequal error protection of convolutional codes

In this paper, we concentrate on the study of combining the optimality with respect to unequal error protection and canonicity of generator matrices for convolutional codes. The transformation which can keep the optimality of generator matrices is constructed, based on which a procedure for obtaining a basic and optimal generator matrix with the smallest external degree is also proposed. Moreover, necessary and sufficient conditions for a canonical generator matrix whose separation vector is the greatest among all canonical generator matrices are given. Finally, the existence of the greatest separation vector among all canonical generator matrices is proved for some convolutional codes.