Extended class of linear feedback shift registers

Shift registers with linear feedback are frequently used. They owe their popularity to very well developed theoretical base. Registers with feedback of prime polynomials are of particular practical importance. They are willingly applied as test sequence generators and test response compactors. The article presents an attempt to extend the class of registers with linear feedback. Basing on the formal description of the register, the algorithms of register transformation are proposed. It allows to obtain the registers with equivalent graphs.[1] I. Gosciniak, “Linear Registers with Mixed Feedback, in Polish; Rejestry liniowe z mieszanym sprzȩżeniem zwrotnym,” Pomiary Automatyka Kontrola, no. 1, pp. 4–6, 1996.[2] K. Iwasaki, “Analysis and proposal of signature circuits for LSI testing,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 7, no. 1, pp. 84–90, 1988.[3] L.-T. Wang, N. Touba, R. Brent, H. Xu, and H. Wang, “On Designing Transformed Linear Feedback Shift Registers with Minimum Hardware Cost – Technical Report,” Computer Engineering Research Center Department of Electrical & Computer Engineering The University of Texas at Austin, 2011.[4] J. Rajski, J. Tyszer, M. Kassab, and N. Mukherjee, “Method for Synthesizing Linear Finite State Machines,” U.S. Patent, No. 6,353,842, 2002.[5] I. Gosciniak, “Equivalent Form of Linear Feedback Shift Registers,” in XIXth National Conference Circuit Theory and Eletronic Networks, 1996, pp. 115–120.[6] L. Alaus, D. Noguet, and J. Palicot, “A Reconfigurable LFSR for Tristandard SDR Transceiver, Architecture and Complexity Analysis,” in Digital System Design Architectures, Methods and Tools, 2008. DSD ’08. 11th EUROMICRO Conference on. IEEE Computer Society, 2008, pp. 61–67.[7] R. Ash, Information Theory. John Wiley & Sons, 1967.[8] M. Kopec, “Can Nonlinear Compactors Be Better than Linear Ones?” IEEE Trans. Comput., no. 11, pp. 1275–1282, 1995.[9] A. Gucha and L. Kinney, “Relating the Cyclic Behaviour of Linear Intrainverted Feedback shift Registers,” IEEE Transactions on Computers, vol. 41, no. 9, pp. 1088–1100, 1992