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On cycle-free lattices with high rate label codes
1. | Department of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran, Iran |
References:
[1] |
A. H. Banihashemi and F. R. Kschischang, Tanner graphs for block codes and lattices: construction and complexity, IEEE Trans. Information Theory, 47 (2001), 822-834.
doi: 10.1109/18.910592. |
[2] |
R. de Buda, Some optimal codes have structre, IEEE Trans. Information Theory, 7 (1989), 893-899. |
[3] |
Y.-S. Choi, I.-J. Baik and S.-Y. Chung, Iterative decoding for low-density parity-check lattices, ICACT, (2008), 358-361. |
[4] |
J. H. Conway and N. J. A. Sloane, "Sphere Packing, Lattices and Groups," 3rd edition, Springer-Verlag, New York, 1998. |
[5] |
T. Etzion, A. Trachtenberg and A. Vardy, Which codes have cycle-free Tanner graphs?, IEEE Trans. Information Theory, 45 (1999), 2173-2181.
doi: 10.1109/18.782170. |
[6] |
G. D. Forney, Jr., Density/length profiles and trellis complexity of lattices, IEEE Trans. Information Theory, 40 (1994), 1753-1774.
doi: 10.1109/18.340453. |
[7] |
G. D. Forney, Jr., M. D. Trott and S. Chung, Sphere-bound-achieving coset codes and multilevel coset codes, IEEE Trans. Information Theory, 46 (2000), 820-850.
doi: 10.1109/18.841165. |
[8] |
R. G. Gallager, Low-density parity-check codes, Ire Trans. Information Theory, IT-8 (1962), 21-28.
doi: 10.1109/TIT.1962.1057683. |
[9] |
X.-Y. Hu, E. Eleftherou and D. M. Arnold, Regular and irregular progressive edge-growth Tanner graphs, IEEE Trans. Information Theory, 51 (2005), 386-398.
doi: 10.1109/TIT.2004.839541. |
[10] |
F. R. Kschischang, B. J. Frey and H. Loeliger, Factor graphs and the sum-product algorithm, IEEE Trans. Information Theory, 47 (2001), 498-519.
doi: 10.1109/18.910572. |
[11] |
M. R. Sadeghi, A. H. Banihashemi and D. Panario, Low-density parity-check lattices: construction and decoding complexity, IEEE Trans. Information Theory, 52 (2006), 4481-4495.
doi: 10.1109/TIT.2006.881720. |
[12] |
M. R. Sadeghi and D. Panario, Low density parity check lattices based on construction $D'$ and cycle-free Tanner graphs, Algebraic Coding Theory and Information Theory, AMS DIMACS, 28 (2005), 85-95. |
[13] |
N. Sommer, M. Feder and O. Shalvi, Low-density lattice codes, IEEE Trans. Information Theory, 54 (2008), 1561-1586.
doi: 10.1109/TIT.2008.917684. |
[14] |
R. M. Tanner, A recursive approach to low-complexity codes, IEEE Trans. Information Theory, 27 (1981), 533-547.
doi: 10.1109/TIT.1981.1056404. |
[15] |
N. Wiberg, "Codes and Decoding on General Graphs," Ph.D thesis, Univ. Linköping, Linköping, Sweden, 1996. |
show all references
References:
[1] |
A. H. Banihashemi and F. R. Kschischang, Tanner graphs for block codes and lattices: construction and complexity, IEEE Trans. Information Theory, 47 (2001), 822-834.
doi: 10.1109/18.910592. |
[2] |
R. de Buda, Some optimal codes have structre, IEEE Trans. Information Theory, 7 (1989), 893-899. |
[3] |
Y.-S. Choi, I.-J. Baik and S.-Y. Chung, Iterative decoding for low-density parity-check lattices, ICACT, (2008), 358-361. |
[4] |
J. H. Conway and N. J. A. Sloane, "Sphere Packing, Lattices and Groups," 3rd edition, Springer-Verlag, New York, 1998. |
[5] |
T. Etzion, A. Trachtenberg and A. Vardy, Which codes have cycle-free Tanner graphs?, IEEE Trans. Information Theory, 45 (1999), 2173-2181.
doi: 10.1109/18.782170. |
[6] |
G. D. Forney, Jr., Density/length profiles and trellis complexity of lattices, IEEE Trans. Information Theory, 40 (1994), 1753-1774.
doi: 10.1109/18.340453. |
[7] |
G. D. Forney, Jr., M. D. Trott and S. Chung, Sphere-bound-achieving coset codes and multilevel coset codes, IEEE Trans. Information Theory, 46 (2000), 820-850.
doi: 10.1109/18.841165. |
[8] |
R. G. Gallager, Low-density parity-check codes, Ire Trans. Information Theory, IT-8 (1962), 21-28.
doi: 10.1109/TIT.1962.1057683. |
[9] |
X.-Y. Hu, E. Eleftherou and D. M. Arnold, Regular and irregular progressive edge-growth Tanner graphs, IEEE Trans. Information Theory, 51 (2005), 386-398.
doi: 10.1109/TIT.2004.839541. |
[10] |
F. R. Kschischang, B. J. Frey and H. Loeliger, Factor graphs and the sum-product algorithm, IEEE Trans. Information Theory, 47 (2001), 498-519.
doi: 10.1109/18.910572. |
[11] |
M. R. Sadeghi, A. H. Banihashemi and D. Panario, Low-density parity-check lattices: construction and decoding complexity, IEEE Trans. Information Theory, 52 (2006), 4481-4495.
doi: 10.1109/TIT.2006.881720. |
[12] |
M. R. Sadeghi and D. Panario, Low density parity check lattices based on construction $D'$ and cycle-free Tanner graphs, Algebraic Coding Theory and Information Theory, AMS DIMACS, 28 (2005), 85-95. |
[13] |
N. Sommer, M. Feder and O. Shalvi, Low-density lattice codes, IEEE Trans. Information Theory, 54 (2008), 1561-1586.
doi: 10.1109/TIT.2008.917684. |
[14] |
R. M. Tanner, A recursive approach to low-complexity codes, IEEE Trans. Information Theory, 27 (1981), 533-547.
doi: 10.1109/TIT.1981.1056404. |
[15] |
N. Wiberg, "Codes and Decoding on General Graphs," Ph.D thesis, Univ. Linköping, Linköping, Sweden, 1996. |
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