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Realization of 2D (2,2)–Periodic Encoders by Means of 2D Periodic Separable Roesser Models

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International Journal of Applied Mathematics and Computer Science
Information Technology for Systems Research (special section, pp. 427-515), Piotr Kulczycki, Janusz Kacprzyk, László T. Kóczy, Radko Mesiar (Eds.)

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Aleixo, J.C. and Rocha, P. (2017). Roesser model representation of 2D periodic behaviors: The (2,2)-periodic SISO case, 10th International Workshop on Multidimensional (nD) Systems (nDS), Zielona Góra, Poland, pp. 1–6.10.1109/NDS.2017.8070617Search in Google Scholar

Aleixo, J.C. and Rocha, P. (2018). On the state space realization of separable periodic 2D systems, 2018 European Control Conference, Limassol, Cyprus, pp. 2300–2305.10.23919/ECC.2018.8550553Search in Google Scholar

Aleixo, J.C., Rocha, P. and Willems, J.C. (2011). State space representation of SISO periodic behaviors, 2011 50th IEEE Conference on Decision and Control/European Control Conference, Orlando, FL, USA, pp. 1545–1550.10.1109/CDC.2011.6160552Search in Google Scholar

Basu, S. and Swamy, M.N.S. (2002). Editorial preface to special issue on multidimensional signals and systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications49(6): 709–714.10.1109/TCSI.2002.1010026Search in Google Scholar

Charoenlarpnopparut, C. and Bose, N. (2001). Grobner bases for problem solving in multidimensional systems, Multidimensional Systems and Signal Processing12(3): 365–376.10.1023/A:1011965825246Search in Google Scholar

Climent, J.-J., Herranz, V., Perea, C. and Tomás, V. (2009). A systems theory approach to periodically time-varying convolutional codes by means of their invariant equivalent, in M. Bras-Amorós and T. Høholdt (Eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer, Berlin/Heidelberg, pp. 73–82.10.1007/978-3-642-02181-7_8Search in Google Scholar

Costello, D.J. (1974). Free distance bounds for convolutional codes, IEEE Transactions on Information Theory20(3): 356–365.10.1109/TIT.1974.1055223Search in Google Scholar

Felstrom, A.J. and Zigangirov, K.S. (1999). Time-varying periodic convolutional codes with low-density parity-check matrix, IEEE Transactions on Information Theory45(6): 2181–2191.10.1109/18.782171Search in Google Scholar

Fornasini, E., Pinho, T., Pinto, R. and Rocha, P. (2015). Minimal realizations of syndrome formers of a special class of 2D codes, in R. Pinto et al. (Eds), Coding Theory and Applications, Springer International Publishing, Cham, pp. 185–193.10.1007/978-3-319-17296-5_19Search in Google Scholar

Fornasini, E. and Pinto, R. (2004). Matrix fraction descriptions in convolutional coding, Linear Algebra and Its Applications392(C): 119–158.10.1016/j.laa.2004.06.007Search in Google Scholar

Fornasini, E. and Valcher, M. (1994). Algebraic aspects of two-dimensional convolutional codes, IEEE Transactions on Information Theory40(4): 1068–1082.10.1109/18.335967Search in Google Scholar

Fornasini, E. and Valcher, M. (1998). Multidimensional systems with finite support behaviors: Signal structure, generation and detection, SIAM Journal on Control and Optimization36(2): 760–779.10.1137/S0363012995292044Search in Google Scholar

Galkowski, K. (1996). The Fornasini–Marchesini and the Roesser models: Algebraic methods for recasting, IEEE Transactions on Automatic Control41(1): 107–112.10.1109/9.481611Search in Google Scholar

Galkowski, K. (2001). State-Space Realisations of Linear 2-D Systems with Extensions to the General nD (n > 2) Case, Vol. 263, Lecture Notes in Control and Information Sciences, Springer, London.Search in Google Scholar

Gluesing-Luersen, H., Rosenthal, J. and Weiner, P. (2000). Duality between mutidimensinal convolutional codes and systems, in F. Colonius et al. (Eds), Advances in Mathematical Systems Theory: A Volume in Honor of Diedrich Hinrichsen, Birkhauser, Boston, MA, pp. 135–150.10.1007/978-1-4612-0179-3_8Search in Google Scholar

Gluesing-Luerssen, H. and Schneider, G. (2007). State space realizations and monomial equivalence for convolutional codes, Linear Algebra and Its Applications425(2): 518–533.10.1016/j.laa.2007.03.004Search in Google Scholar

Guardia, G.G.L. (2019). Asymptotically good convolutional codes, Linear and Multilinear Algebra67(7): 1483–1494.10.1080/03081087.2018.1459448Search in Google Scholar

Hinamoto, T. (1980). Realizations of a state-space model from two-dimensional input-output map, IEEE Transactions on Circuits and Systems27(1): 36–44.10.1109/TCS.1980.1084713Search in Google Scholar

Jangisarakul, P. and Charoenlarpnopparut, C. (2011). Algebraic decoder of multidimensional convolutional code: Constructive algorithms for determining syndrome decoder and decoder matrix based on Grobner basis, Multidimensional Systems and Signal Processing22(1): 67–81.10.1007/s11045-010-0139-7Search in Google Scholar

Kaczorek, T. (2001). Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks, International Journal of Applied Mathematics and Computer Science11(2): 369–376.Search in Google Scholar

Kailath, T. (1980). Linear Systems, Prentice-Hall, Englewood Cliffs, NJ.Search in Google Scholar

Kuijper, M. and Polderman, J. (2004). Reed–Solomon list decoding from a system theoretic perspective, IEEE Transactions on Information TheoryIT-50(2): 259–271.10.1109/TIT.2003.822593Search in Google Scholar

Kuijper, M. and Willems, J.C. (1997). A behavioral framework for periodically time varying systems, Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, USA, Vol. 3, pp. 2013–2016.Search in Google Scholar

Lobo, R., Bitzer, D.L. and Vouk, M.A. (2012). On locally invertible encoders and multidimensional convolutional codes, IEEE Transactions on Information Theory58(3): 1774–1782.10.1109/TIT.2011.2178129Search in Google Scholar

Mooser, M. (1983). Some periodic convolutional codes better than any fixed code (corresp.), IEEE Transactions on Information Theory29(5): 750–751.10.1109/TIT.1983.1056727Search in Google Scholar

Napp, D., Perea, C. and Pinto, R. (2010). Input-state-output representations and constructions of finite support 2D convolutional codes, Advances in Mathematics of Communications4(4): 533–545.10.3934/amc.2010.4.533Search in Google Scholar

Napp, D., Pereira, R., Pinto, R. and Rocha, P. (2019). Periodic state-space representations of periodic convolutional codes, Cryptography and Communications11(4): 585–595.10.1007/s12095-018-0313-6Search in Google Scholar

Palazzo, R. (1993). A time-varying convolutional encoder better than the best time-invariant encoder, IEEE Transactions on Information Theory39(3): 1109–1110.10.1109/18.256526Search in Google Scholar

Pinho, T. (2016). Minimal State-Space Realizations of 2D Convolutional Codes, PhD thesis, University of Aveiro, Aveiro.10.1007/978-3-319-10380-8_2Search in Google Scholar

Pinho, T., Pinto, R. and Rocha, P. (2014). Realization of 2D convolutional codes of rate 1/n by separable Roesser models, Designs, Codes and Cryptography70(1): 241–250.10.1007/s10623-012-9768-1Search in Google Scholar

Rosenthal, J. (2001). Connections between linear systems and convolutional codes, in B. Marcus and J. Rosenthal (Eds), Codes, Systems and Graphical Models, Springer-Verlag, New York, NY, pp. 39–66.10.1007/978-1-4613-0165-3_2Search in Google Scholar

Rosenthal, J. and York, E.V. (1999). BCH convolutional codes, IEEE Transactions on Automatic Control45(6): 1833–1844.10.1109/18.782104Search in Google Scholar

Valcher, M. and Fornasini, E. (1994). On 2D finite support convolutional codes: An algebraic approach, Multidimensional Systems and Signal Processing5(3): 231–243.10.1007/BF00980707Search in Google Scholar

Weiner, P. (1998). Multidimensional Convolutional Codes, PhD dissertation, University of Notre Dame, South Bend, IN.Search in Google Scholar

Zerz, E. (2000). Topics in Multidimensional Linear Systems Theory, Lecture Notes in Control and Information Sciences, Vol. 256, Springer-Verlag, London.Search in Google Scholar

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2083-8492
Language:
English
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Journal Subjects:
Mathematics, Applied Mathematics