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Decoding of $2$D convolutional codes over an erasure channel
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1. | Department of Information Engineering, University of Padua, Italy |
2. | CIDMA, Department of Mathematics, University of Aveiro, Portugal, Portugal |
3. | SYSTEC, Faculty of Engineering, University of Porto, Portugal |
References:
[1] |
S. Attasi, Systèmes linéaires homogènes à deux indices, in Rapport Laboria, 1973. |
[2] |
E. Fornasini and G. Marchesini, Algebraic realization theory of two-dimensional filters, in Variable Structure Systems with Application to Economics and Biology (eds. A. Ruberti and R. Mohler), Springer, 1975, 64-82. |
[3] |
E. Fornasini and R. Pinto, Matrix fraction descriptions in convolutional coding, Linear Algebra Appl., 392 (2004), 119-158.
doi: 10.1016/j.laa.2004.06.007. |
[4] |
E. Fornasini and M. E. Valcher, Algebraic aspects of two-dimensional convolutional codes, IEEE Trans. Inf. Theory, 40 (1994), 1068-1082.
doi: 10.1109/18.335967. |
[5] |
G. Forney, Convolutional Codes I: Algebraic structure, IEEE Trans. Inf. Theory, 16 (1970), 720-738. Correction, Ibid., 17 (1971), 360. |
[6] |
G. Forney, Structural analysis of convolutional codes via dual codes, IEEE Trans. Inf. Theory, 19 (1973), 512-518. |
[7] |
B. Levy, 2D Polynomial and Rational Matrices, and their Applications for the Modeling of 2-D Dynamical Systems, Ph.D thesis, Stanford University, USA, 1981. |
[8] |
T. Lin, M. Kawamata and T. Higuchi, Decomposition of 2-D separable-denominator systems: Existence, uniqueness, and applications, IEEE Trans. Circ. Syst., 34 (1987), 292-296.
doi: 10.1109/TCS.1987.1086219. |
[9] |
T. Pinho, Minimal State-Space Realizations of 2D Convolutional Codes, Ph.D thesis, Univ. Aveiro, Portugal, 2014. |
[10] |
T. Pinho, R. Pinto and P. Rocha, Realization of 2D convolutional codes of rate $\frac1n$ by separable Roesser models, Des. Codes Crypt., 70 (2014), 241-250.
doi: 10.1007/s10623-012-9768-1. |
[11] |
P. Rocha, Representation of noncausal 2D systems, in New Trends in Systems Theory, Birkhäuser, 1991, 630-635. |
[12] |
R. P. Roesser, A Discrete State-Space Model for Linear Image Processing, IEEE Trans. Automat. Control, 20 (1975), 1-10. |
[13] |
M. E. Valcher and E. Fornasini, On 2D finite support convolutional codes, Multidim. Syst. Signal Proc., 5 (1994), 231-243.
doi: 10.1007/BF00980707. |
[14] |
P. A. Weiner, Multidimensional Convolutional Codes, Ph.D thesis, Univ. Notre Dame, USA, 1998. |
[15] |
J. C. Willems, Models for dynamics, in Dynamics Reported (eds. U. Kirchgraber and H.O. Walther), John Wiley Sons Ltd., 1989, 171-269. |
show all references
References:
[1] |
S. Attasi, Systèmes linéaires homogènes à deux indices, in Rapport Laboria, 1973. |
[2] |
E. Fornasini and G. Marchesini, Algebraic realization theory of two-dimensional filters, in Variable Structure Systems with Application to Economics and Biology (eds. A. Ruberti and R. Mohler), Springer, 1975, 64-82. |
[3] |
E. Fornasini and R. Pinto, Matrix fraction descriptions in convolutional coding, Linear Algebra Appl., 392 (2004), 119-158.
doi: 10.1016/j.laa.2004.06.007. |
[4] |
E. Fornasini and M. E. Valcher, Algebraic aspects of two-dimensional convolutional codes, IEEE Trans. Inf. Theory, 40 (1994), 1068-1082.
doi: 10.1109/18.335967. |
[5] |
G. Forney, Convolutional Codes I: Algebraic structure, IEEE Trans. Inf. Theory, 16 (1970), 720-738. Correction, Ibid., 17 (1971), 360. |
[6] |
G. Forney, Structural analysis of convolutional codes via dual codes, IEEE Trans. Inf. Theory, 19 (1973), 512-518. |
[7] |
B. Levy, 2D Polynomial and Rational Matrices, and their Applications for the Modeling of 2-D Dynamical Systems, Ph.D thesis, Stanford University, USA, 1981. |
[8] |
T. Lin, M. Kawamata and T. Higuchi, Decomposition of 2-D separable-denominator systems: Existence, uniqueness, and applications, IEEE Trans. Circ. Syst., 34 (1987), 292-296.
doi: 10.1109/TCS.1987.1086219. |
[9] |
T. Pinho, Minimal State-Space Realizations of 2D Convolutional Codes, Ph.D thesis, Univ. Aveiro, Portugal, 2014. |
[10] |
T. Pinho, R. Pinto and P. Rocha, Realization of 2D convolutional codes of rate $\frac1n$ by separable Roesser models, Des. Codes Crypt., 70 (2014), 241-250.
doi: 10.1007/s10623-012-9768-1. |
[11] |
P. Rocha, Representation of noncausal 2D systems, in New Trends in Systems Theory, Birkhäuser, 1991, 630-635. |
[12] |
R. P. Roesser, A Discrete State-Space Model for Linear Image Processing, IEEE Trans. Automat. Control, 20 (1975), 1-10. |
[13] |
M. E. Valcher and E. Fornasini, On 2D finite support convolutional codes, Multidim. Syst. Signal Proc., 5 (1994), 231-243.
doi: 10.1007/BF00980707. |
[14] |
P. A. Weiner, Multidimensional Convolutional Codes, Ph.D thesis, Univ. Notre Dame, USA, 1998. |
[15] |
J. C. Willems, Models for dynamics, in Dynamics Reported (eds. U. Kirchgraber and H.O. Walther), John Wiley Sons Ltd., 1989, 171-269. |
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