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On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$
Codes on planar Tanner graphs
1. | Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India, India |
References:
[1] |
J. A. Bondy and U. S. R. Murty, "Graph Theory with Applications,'' North-Holland, 1976. |
[2] |
V. Y. Chernyak and M. Chertkov, Planar graphical models which are easy, J. Statist. Mechan. Theory Exper., 2010 (2010), p. P11007.
doi: 10.1088/1742-5468/2010/11/P11007. |
[3] |
M. Chertkov, V. Y. Chernyak and R. Teodorescu, Belief propagation and loop series on planar graphs, J. Statist. Mechan. Theory Exper., 2008 (2008), p. P05003.
doi: 10.1088/1742-5468/2008/05/P05003. |
[4] |
K. Diks, H. N. Djidjev, O. Sykora and I. Vrto, Edge separators of planar and outerplanar graphs with applications, J. Algorithms, 14 (1993), 258-279.
doi: 10.1006/jagm.1993.1013. |
[5] |
T. Etzion, A. Trachtenberg and A. Vardy, Which codes have cycle-free Tanner graphs?, IEEE Trans. Inform. Theory, 45 (1999), 2173-2181.
doi: 10.1109/18.782170. |
[6] |
V. Gómez, H. J. Kappen and M. Chertkov, Approximate inference on planar graphs using loop calculus and belief propagation, J. Mach. Learn. Res., 99 (2010), 1273-1296. |
[7] |
F. Harary, "Graph Theory,'' Addison-Wesley Publishers, 1969. |
[8] |
N. Kashyap, Code decomposition: theory and applications, in "IEEE International Symposium on Information Theory,'' (2007), 481-485.
doi: 10.1109/ISIT.2007.4557271. |
[9] |
N. Kashyap, A decomposition theory for binary linear codes, IEEE Trans. Inform. Theory, 54 (2008), 3035-3058.
doi: 10.1109/TIT.2008.924700. |
[10] |
R. J. Lipton and R. E. Tarjan, Applications of a planar separator theorem, in "18th Annual Symposium on Foundations of Computer Science,'' (1977), 162-170.
doi: 10.1109/SFCS.1977.6. |
[11] |
S. Srinivasan and A. Thangaraj, Codes that have Tanner graphs with non-overlapping cycles, in "5th International Symposium on Turbo Codes and Related Topics,'' (2008), 299-304. |
[12] |
B. Xiang, R. Shen, A. Pan, D. Bao and X. Zeng, An area-efficient and low-power multirate decoder for quasi-cyclic low-density parity-check codes, IEEE Trans. Very Large Scale Integr. Systems, 18 (2010), 1447-1460.
doi: 10.1109/TVLSI.2009.2025169. |
[13] |
C. Zhang, Z. Wang, J. Sha, L. Li and J. Lin, Flexible LDPC decoder design for multigigabit-per-second applications, IEEE Trans. Circ. Systems I, 57 (2010), 116-124.
doi: 10.1109/TCSI.2009.2018915. |
show all references
References:
[1] |
J. A. Bondy and U. S. R. Murty, "Graph Theory with Applications,'' North-Holland, 1976. |
[2] |
V. Y. Chernyak and M. Chertkov, Planar graphical models which are easy, J. Statist. Mechan. Theory Exper., 2010 (2010), p. P11007.
doi: 10.1088/1742-5468/2010/11/P11007. |
[3] |
M. Chertkov, V. Y. Chernyak and R. Teodorescu, Belief propagation and loop series on planar graphs, J. Statist. Mechan. Theory Exper., 2008 (2008), p. P05003.
doi: 10.1088/1742-5468/2008/05/P05003. |
[4] |
K. Diks, H. N. Djidjev, O. Sykora and I. Vrto, Edge separators of planar and outerplanar graphs with applications, J. Algorithms, 14 (1993), 258-279.
doi: 10.1006/jagm.1993.1013. |
[5] |
T. Etzion, A. Trachtenberg and A. Vardy, Which codes have cycle-free Tanner graphs?, IEEE Trans. Inform. Theory, 45 (1999), 2173-2181.
doi: 10.1109/18.782170. |
[6] |
V. Gómez, H. J. Kappen and M. Chertkov, Approximate inference on planar graphs using loop calculus and belief propagation, J. Mach. Learn. Res., 99 (2010), 1273-1296. |
[7] |
F. Harary, "Graph Theory,'' Addison-Wesley Publishers, 1969. |
[8] |
N. Kashyap, Code decomposition: theory and applications, in "IEEE International Symposium on Information Theory,'' (2007), 481-485.
doi: 10.1109/ISIT.2007.4557271. |
[9] |
N. Kashyap, A decomposition theory for binary linear codes, IEEE Trans. Inform. Theory, 54 (2008), 3035-3058.
doi: 10.1109/TIT.2008.924700. |
[10] |
R. J. Lipton and R. E. Tarjan, Applications of a planar separator theorem, in "18th Annual Symposium on Foundations of Computer Science,'' (1977), 162-170.
doi: 10.1109/SFCS.1977.6. |
[11] |
S. Srinivasan and A. Thangaraj, Codes that have Tanner graphs with non-overlapping cycles, in "5th International Symposium on Turbo Codes and Related Topics,'' (2008), 299-304. |
[12] |
B. Xiang, R. Shen, A. Pan, D. Bao and X. Zeng, An area-efficient and low-power multirate decoder for quasi-cyclic low-density parity-check codes, IEEE Trans. Very Large Scale Integr. Systems, 18 (2010), 1447-1460.
doi: 10.1109/TVLSI.2009.2025169. |
[13] |
C. Zhang, Z. Wang, J. Sha, L. Li and J. Lin, Flexible LDPC decoder design for multigigabit-per-second applications, IEEE Trans. Circ. Systems I, 57 (2010), 116-124.
doi: 10.1109/TCSI.2009.2018915. |
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