Focus on theoretical properties of blind convolutional codes identification methods based on rank criterion

In the cognitive radio field, the receiver should be able to perform a blind identification of the encoder parameters used by the transmitter from the only knowledge of the received data stream. In this context, the most methods dedicated to the blind identification of the parameters of error correcting codes are based on the rank calculation of matrices formed from the received data stream. Nevertheless, the theoretical behaviour of the rank criterion has neither been justified nor demonstrated. In this paper, we propose an algebraic and theoretical study of the rank criterion behaviour that allows us to identify the convolutional codes parameters and we investigate some encoder dependent properties that generate multiple rank deficiencies.