1 Algebraic method for blind recovery of punctured convolutional encoders from an erroneous bitstream M´ elanie Marazin 1-2 Roland Gautier 1-2 Gilles Burel 1-2 1 Universit´ e Europ´ eenne de Bretagne, France. 2 Universit´ e de Brest; CNRS, UMR 3192 Lab-STICC, ISSTB, 6 avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3, France Abstract—To enhance the quality of transmissions, all digital communication systems use error-correcting codes. By introduc- ing some redundancy in the informative binary data stream, they allow one to better withstand channel impairments. The design of new coding schemes leads to a perpetual evolution of the digital communication systems and, thus, cognitive radio receivers have to be designed. Such receivers will be able to blind estimate the transmitter parameters. In this study, an algebraic method dedicated to the blind identification of punctured convolutional encoders is presented. The blind identification of such encoders is of great interest, because convolutional encoders are embedded in most digital transmission systems where the puncturing principle is used to increase the code rate in order to reduce the loss of the information data rate due to the redundancy introduced by the encoder. After a brief recall of the principle of puncturing codes and the construction of the equivalent punctured code, a new method dedicated to the blind identification of both the mother code and the puncturing pattern is developed when the received bits are erroneous. Finally, case-studies are presented to illustrate the performances of our blind identification method. I. I NTRODUCTION In most digital transmission systems, error-correcting codes are used for enhancement of the communication quality. These codes introduced some redundancy in the informative binary data stream to better withstand channel impairments. In this paper the problem of the blind identification of error correcting codes is treated. This problem has for a long time been reserved for military applications such as passive listening. In such a context, the adversary has only access to the intercepted noise bits stream with no knowledge of the parameters of the code. Therefore, these parameters must be blindly estimated. Such methods are also used in cryptanalysis systems. In this context, the objective is to recover the original message. But, many methods are based on the hypothesis that they have access to a decoded message. So, to obtain this decoded message it is necessary to know the encoder. Moreover, in [1], the author proposed a library which allows a good security level for peer to peer data transmission using convolutional codes punctured (or not) with controlled additive noise. Currently, with the aim of enhancing the quality of transmis- sion, new coding schemes are constantly being developed. In such a context, it is more and more difficult for users to follow all the changes to stay up-to-date and also to have an electronic communication device which is always compatible with every standard in use all around the world. Consequently, it becomes necessary to design cognitive receivers. In literature a lot of works deal with the domain of cognitive radio. Generally, a Email: {melanie.marazin, roland.gautier, gilles.burel}@univ-brest.fr cognitive radio device has the ability to dynamically select their configuration parameters, on the transmitter side. Thus, a cognitive transmitter is able to adapt the encoder to the transmission channel, among a set of encoders. Here, the problem of a self-reconfigurable cognitive receiver is treated. Such receivers will be able to blindly estimate the transmitter parameters simply from the knowledge of the received data. In this paper, the blind identification problem of error- correcting codes is considered for cognitive radio receiver design. Here, among the error-correcting codes, the blind recovery of convolutional encoders is dealt with. In a noisy environment, the first approach to identify the parameters of a code is related in [2]. At the same time, methods to recover a block code are developed in [3], [4] whereas [5] deals with to the blind identification of linear scramble. In [6], an iterative algorithm dedicated to the blind identification of a rate (n − 1)/n convolutional encoder is presented. In [7], [8], the authors are interested in the identification of the interleaver of a turbo-code. An algorithm to decide if the sequence is coded by a linear code is presented in [9]. The redundancy introduced by a convolutional encoder pro- duces a decrease in the transmission rate. A simple technique, called puncturing, allows an increase in the code rate. It consists of deleting some symbols from an encoded word. This technique is usually used in digital communication systems. In a noisy environment (i.e when the received bits are erroneous), this paper deals with the blind identification of the punc- tured convolutional encoder. The first approaches developed to recover the punctured code in a noiseless context were proposed in [10], [11]. The new method presented in [12] deals with the specific case of a rate 1/n mother code in a noisy environment. Here, this paper describes a new iterative method for blind recognition of a rate k/n punctured convolutional code. In this context, the blind identification of a punctured code corresponds to the blind identification of the mother code and the puncturing pattern. This paper is organized as follows. In Sect. II, the prin- ciple of punctured convolutional encoders is explained. The description of the blind recognition of this punctured code is developed in Sect. III. Finally, the performances of the blind identification method are discussed in Sect. IV. Conclusions and prospects are drawn in Sect. V. II. PUNCTURED CONVOLUTIONAL CODE The concept of punctured convolutional code was intro- duced by Cain [13] in 1979. Such a high-rate code is obtained This paper is a postprint of a paper submitted to and accepted for publication in IET Signal Processing and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library hal-00714044, version 1 - 3 Jul 2012 Author manuscript, published in "Iet Signal Processing 6, 2 (2012) 122-131" DOI : 10.1049/iet-spr.2010.0343