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Decoding of $2$D convolutional codes over an erasure channel
1. | Departament de Matemàtiques, Universitat d'Alacant, Ap. Correus 99, E-03080, Alacant |
2. | CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal, Portugal, Portugal |
References:
[1] |
P. Almeida, D. Napp and R. Pinto, A new class of superregular matrices and MDP convolutional codes, Linear Algebra Appl., 439 (2013), 2145-2157.
doi: 10.1016/j.laa.2013.06.013. |
[2] |
M. Arai, A. Yamamoto, A. Yamaguchi, S. Fukumoto and K. Iwasaki, Analysis of using convolutional codes to recover packet losses over burst erasure channels, in Proc. 2001 Pacific Rim Int. Symp. Depend. Comp., IEEE, Seoul, 2001, 258-265.
doi: 10.1109/PRDC.2001.992706. |
[3] |
J. J. Climent, D. Napp, C. Perea and R. Pinto, A construction of MDS 2D convolutional codes of rate 1/n based on superregular matrices, Linear Algebra Appl., 437 (2012), 766-780.
doi: 10.1016/j.laa.2012.02.032. |
[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] |
E. Fornasini and M. E. Valcher, On 2D finite support convolutional codes: an algebraic approach, Multidim. Syst. Signal Proc., 5 (1994), 231-243.
doi: 10.1007/BF00980707. |
[6] |
E. Fornasini and M. E. Valcher, nD polynomial matrices with applications to multidimensional signal analysis, Multidim. Syst. Signal Proc., 8 (1997), 387-407.
doi: 10.1023/A:1008256224288. |
[7] |
H. Gluesing-Luerssen, J. Rosenthal and R. Smarandache, Strongly MDS convolutional codes, IEEE Trans. Inf. Theory, 52 (2006), 584-598.
doi: 10.1109/TIT.2005.862100. |
[8] |
H. Gluesing-Luerssen, J. Rosenthal and P. Weiner, Duality between multidimensional convolutional codes and systems, in Advances in Mathematical Systems Theory (eds. F. Colonius, U. Helmke, F. Wirth and D. Praetzel-Wolters), Birkhauser, 2000, 135-150.
doi: 10.1007/978-1-4612-0179-3_8. |
[9] |
R. Hutchinson, The existence of strongly MDS convolutional codes, SIAM J. Control Opt., 47 (2008), 2812-2826.
doi: 10.1137/050638977. |
[10] |
R. Hutchinson, J. Rosenthal and R. Smarandache, Convolutional codes with maximum distance profile, Syst. Control Lett., 54 (2005), 53-63.
doi: 10.1016/j.sysconle.2004.06.005. |
[11] |
R. Hutchinson, R. Smarandache and J. Trumpf, On superregular matrices and MDP convolutional codes, Linear Algebra Appl., 428 (2008), 2585-2596.
doi: 10.1016/j.laa.2008.02.011. |
[12] |
P. Jangisarakul and C. Charoenlarpnopparut, Algebraic decoder of multidimensional convolutional code: Constructive algorithms for determining syndrome decoder and decoder matrix based on Gröbner basis, Multidim. Syst. Signal Proc., 22 (2011), 67-81.
doi: 10.1007/s11045-010-0139-7. |
[13] |
D. Napp, C. Perea and R. Pinto, Input-state-output representations and constructions of finite support 2D convolutional codes, Adv. Math. Commun., 4 (2010), 533-545.
doi: 10.3934/amc.2010.4.533. |
[14] |
V. Tomás, Complete-MDP Convolutional Codes over the Erasure Channel, Ph.D thesis, Univ. Alicante, Alicante, Spain, 2010. |
[15] |
V. Tomás, J. Rosenthal and R. Smarandache, Reverse-maximum distance profile convolutional codes over the erasure channel, in Proc.19th Int. Symp. Math. Theory Netw. Syst. (ed. A. Edelmayer), 2010, 2121-2127.
doi: 10.5167/uzh-44714. |
[16] |
V. Tomás, J. Rosenthal and R. Smarandache, Decoding of convolutional codes over the erasure channel, IEEE Trans. Inf. Theory, 58 (2012), 90-108.
doi: 10.1109/TIT.2011.2171530. |
[17] |
P. A. Weiner, Multidimensional Convolutional Codes, Ph.D thesis, Univ. Notre Dame, Indiana, USA, 1998. |
show all references
References:
[1] |
P. Almeida, D. Napp and R. Pinto, A new class of superregular matrices and MDP convolutional codes, Linear Algebra Appl., 439 (2013), 2145-2157.
doi: 10.1016/j.laa.2013.06.013. |
[2] |
M. Arai, A. Yamamoto, A. Yamaguchi, S. Fukumoto and K. Iwasaki, Analysis of using convolutional codes to recover packet losses over burst erasure channels, in Proc. 2001 Pacific Rim Int. Symp. Depend. Comp., IEEE, Seoul, 2001, 258-265.
doi: 10.1109/PRDC.2001.992706. |
[3] |
J. J. Climent, D. Napp, C. Perea and R. Pinto, A construction of MDS 2D convolutional codes of rate 1/n based on superregular matrices, Linear Algebra Appl., 437 (2012), 766-780.
doi: 10.1016/j.laa.2012.02.032. |
[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] |
E. Fornasini and M. E. Valcher, On 2D finite support convolutional codes: an algebraic approach, Multidim. Syst. Signal Proc., 5 (1994), 231-243.
doi: 10.1007/BF00980707. |
[6] |
E. Fornasini and M. E. Valcher, nD polynomial matrices with applications to multidimensional signal analysis, Multidim. Syst. Signal Proc., 8 (1997), 387-407.
doi: 10.1023/A:1008256224288. |
[7] |
H. Gluesing-Luerssen, J. Rosenthal and R. Smarandache, Strongly MDS convolutional codes, IEEE Trans. Inf. Theory, 52 (2006), 584-598.
doi: 10.1109/TIT.2005.862100. |
[8] |
H. Gluesing-Luerssen, J. Rosenthal and P. Weiner, Duality between multidimensional convolutional codes and systems, in Advances in Mathematical Systems Theory (eds. F. Colonius, U. Helmke, F. Wirth and D. Praetzel-Wolters), Birkhauser, 2000, 135-150.
doi: 10.1007/978-1-4612-0179-3_8. |
[9] |
R. Hutchinson, The existence of strongly MDS convolutional codes, SIAM J. Control Opt., 47 (2008), 2812-2826.
doi: 10.1137/050638977. |
[10] |
R. Hutchinson, J. Rosenthal and R. Smarandache, Convolutional codes with maximum distance profile, Syst. Control Lett., 54 (2005), 53-63.
doi: 10.1016/j.sysconle.2004.06.005. |
[11] |
R. Hutchinson, R. Smarandache and J. Trumpf, On superregular matrices and MDP convolutional codes, Linear Algebra Appl., 428 (2008), 2585-2596.
doi: 10.1016/j.laa.2008.02.011. |
[12] |
P. Jangisarakul and C. Charoenlarpnopparut, Algebraic decoder of multidimensional convolutional code: Constructive algorithms for determining syndrome decoder and decoder matrix based on Gröbner basis, Multidim. Syst. Signal Proc., 22 (2011), 67-81.
doi: 10.1007/s11045-010-0139-7. |
[13] |
D. Napp, C. Perea and R. Pinto, Input-state-output representations and constructions of finite support 2D convolutional codes, Adv. Math. Commun., 4 (2010), 533-545.
doi: 10.3934/amc.2010.4.533. |
[14] |
V. Tomás, Complete-MDP Convolutional Codes over the Erasure Channel, Ph.D thesis, Univ. Alicante, Alicante, Spain, 2010. |
[15] |
V. Tomás, J. Rosenthal and R. Smarandache, Reverse-maximum distance profile convolutional codes over the erasure channel, in Proc.19th Int. Symp. Math. Theory Netw. Syst. (ed. A. Edelmayer), 2010, 2121-2127.
doi: 10.5167/uzh-44714. |
[16] |
V. Tomás, J. Rosenthal and R. Smarandache, Decoding of convolutional codes over the erasure channel, IEEE Trans. Inf. Theory, 58 (2012), 90-108.
doi: 10.1109/TIT.2011.2171530. |
[17] |
P. A. Weiner, Multidimensional Convolutional Codes, Ph.D thesis, Univ. Notre Dame, Indiana, USA, 1998. |
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