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Input-state-output representations and constructions of finite support 2D convolutional codes
1. | Department of Mathematics, University of Aveiro, Campus Universitario de Santiago, 3810-193 Aveiro, Portugal, Portugal |
2. | Center of Operation Research, Department of Statistics, Mathematics and Informatics, University Miguel Hernández, Av. Universidad s/n, 0302 Elche, Spain |
References:
[1] |
E. Fornasini and G. Marchesini, Structure and properties of two-dimensional systems, in "Multidimensional Systems, Techniques and Applications'' (ed. S.G. Tzafestas), (1986), 37-88. |
[2] |
E. Fornasini and M. E. Valcher, Algebraic aspects of two-dimensional convolutional codes, IEEE Trans. Inf. Th., 40 (1994), 1068-1082.
doi: 10.1109/18.335967. |
[3] |
H. Gluesing-Luersen, J. Rosenthal and P. A. Weiner, Duality between mutidimensinal convolutional codes and systems, in "Advances in Mathematical Systems Theory, a Volume in Honor of Diedrich Hinrichsen'' (eds. F. Colonius, U. Helmke, F. Wirth and D. Prtzel-Wolters), Birkhuser, Boston, (2000), 135-150. |
[4] |
J. Justesen and S. Forchhammer, Two dimensional information theory and coding. With applications to graphics data and high-density storage media, Cambridge University Press, Cambridge, (2010), 171. |
[5] |
T. Kailath, "Linear Systems,'' Prentice Hall, Englewood Cliffs, NJ, 1980. |
[6] |
B. Kitchens, Multidimensional convolutional codes, SIAM J. Discrete Math., 15 (2002), 367-381.
doi: 10.1137/S0895480100378495. |
[7] |
B. C. Lévy, "2-D Polynomial and Rational Matrices, and their Applications for the Modeling of 2-D Dynamical Systems,'' Ph.D thesis, Stanford University, USA, 1981. |
[8] |
R. G. Lobo, "On Locally Invertible Encoders and Muldimensional Convolutional Codes,'' Ph.D thesis, North Carolina State University, USA, 2006. |
[9] |
P. Rocha, "Structure and Representation of 2-D Systems,'' Ph.D thesis, Groningen University, Holland, 1990. |
[10] |
J. Rosenthal, J. M. Schumacher and E. V. York, On behaviors and convolutional codes, IEEE Trans. Inf. Th., 42 (1996), 1881-1891.
doi: 10.1109/18.556682. |
[11] |
J. Rosenthal and R. Smarandache, Maximum distance separable convolutional codes, Appl. Algebra Engrg. Comm. Comput., 10 (1999), 15-32.
doi: 10.1007/s002000050120. |
[12] |
J. Rosenthal and E. V. York, BCH convolutional codes, IEEE Trans. Inf. Th., 45 (1999), 1833-1844.
doi: 10.1109/18.782104. |
[13] |
J. Singh and M. L. Singh, A new family of two-dimensional codes for optical CDMA systems, Optik - International Journal for Light and Electron Optics, 120 (2009), 959-962. |
[14] |
J. Swartz, T. Pavlidis and Y. P. Wang, Information encoding with two-dimensional bar codes, IEEE Computer Society, 25 (1992), 18-28. |
[15] |
M. E. Valcher and E. Fornasini, On 2D finite support convolutional codes: an algebraic approach, Multidimensional Systems and Signal Processing, 5 (1994), 231-243.
doi: 10.1007/BF00980707. |
[16] |
P. Weiner, "Muldimensional Convolutional Codes,'' Ph.D thesis, University of Notre Dame, USA, 1998. |
[17] |
X.-L. Zhou and Y. Hu, Multilength two-dimensional codes for optical cdma system, Optoelectronics Letters, 1 (2005), 232-234.
doi: 10.1007/BF03033851. |
show all references
References:
[1] |
E. Fornasini and G. Marchesini, Structure and properties of two-dimensional systems, in "Multidimensional Systems, Techniques and Applications'' (ed. S.G. Tzafestas), (1986), 37-88. |
[2] |
E. Fornasini and M. E. Valcher, Algebraic aspects of two-dimensional convolutional codes, IEEE Trans. Inf. Th., 40 (1994), 1068-1082.
doi: 10.1109/18.335967. |
[3] |
H. Gluesing-Luersen, J. Rosenthal and P. A. Weiner, Duality between mutidimensinal convolutional codes and systems, in "Advances in Mathematical Systems Theory, a Volume in Honor of Diedrich Hinrichsen'' (eds. F. Colonius, U. Helmke, F. Wirth and D. Prtzel-Wolters), Birkhuser, Boston, (2000), 135-150. |
[4] |
J. Justesen and S. Forchhammer, Two dimensional information theory and coding. With applications to graphics data and high-density storage media, Cambridge University Press, Cambridge, (2010), 171. |
[5] |
T. Kailath, "Linear Systems,'' Prentice Hall, Englewood Cliffs, NJ, 1980. |
[6] |
B. Kitchens, Multidimensional convolutional codes, SIAM J. Discrete Math., 15 (2002), 367-381.
doi: 10.1137/S0895480100378495. |
[7] |
B. C. Lévy, "2-D Polynomial and Rational Matrices, and their Applications for the Modeling of 2-D Dynamical Systems,'' Ph.D thesis, Stanford University, USA, 1981. |
[8] |
R. G. Lobo, "On Locally Invertible Encoders and Muldimensional Convolutional Codes,'' Ph.D thesis, North Carolina State University, USA, 2006. |
[9] |
P. Rocha, "Structure and Representation of 2-D Systems,'' Ph.D thesis, Groningen University, Holland, 1990. |
[10] |
J. Rosenthal, J. M. Schumacher and E. V. York, On behaviors and convolutional codes, IEEE Trans. Inf. Th., 42 (1996), 1881-1891.
doi: 10.1109/18.556682. |
[11] |
J. Rosenthal and R. Smarandache, Maximum distance separable convolutional codes, Appl. Algebra Engrg. Comm. Comput., 10 (1999), 15-32.
doi: 10.1007/s002000050120. |
[12] |
J. Rosenthal and E. V. York, BCH convolutional codes, IEEE Trans. Inf. Th., 45 (1999), 1833-1844.
doi: 10.1109/18.782104. |
[13] |
J. Singh and M. L. Singh, A new family of two-dimensional codes for optical CDMA systems, Optik - International Journal for Light and Electron Optics, 120 (2009), 959-962. |
[14] |
J. Swartz, T. Pavlidis and Y. P. Wang, Information encoding with two-dimensional bar codes, IEEE Computer Society, 25 (1992), 18-28. |
[15] |
M. E. Valcher and E. Fornasini, On 2D finite support convolutional codes: an algebraic approach, Multidimensional Systems and Signal Processing, 5 (1994), 231-243.
doi: 10.1007/BF00980707. |
[16] |
P. Weiner, "Muldimensional Convolutional Codes,'' Ph.D thesis, University of Notre Dame, USA, 1998. |
[17] |
X.-L. Zhou and Y. Hu, Multilength two-dimensional codes for optical cdma system, Optoelectronics Letters, 1 (2005), 232-234.
doi: 10.1007/BF03033851. |
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