-
Previous Article
Close values of shifted modular inversions and the decisional modular inversion hidden number problem
- AMC Home
- This Issue
-
Next Article
Identifying codes of degree 4 Cayley graphs over Abelian groups
Information--bit error rate and false positives in an MDS code
1. | Department of Algebra and CITIC-UGR, University of Granada, E18071 Granada, Spain, Spain |
2. | Department of Computer Sciences and AI, and CITIC-UGR, University of Granada, E18071 Granada, Spain |
References:
[1] |
C. Desset, B. Macq and L. Vandendorpe, Computing the word-, symbol-, and bit-error rates for block error-correcting codes, IEEE Trans. Commun., 52 (2004), 910-921.
doi: 10.1109/TCOMM.2004.829509. |
[2] |
R. Dodunekova and S. M. Dodunekov, Sufficient conditions for good and proper error-detecting codes, IEEE Trans. Inf. Theory, 43 (1997), 2023-2026.
doi: 10.1109/18.641570. |
[3] |
R. Dodunekova and S. M. Dodunekov, The MMD codes are proper for error detection, IEEE Trans. Inf. Theory, 48 (2002), 3109-3111.
doi: 10.1109/TIT.2002.805082. |
[4] |
R. Dodunekova, S. M. Dodunekov and E. Nikolova, A survey on proper codes, Discrete Appl. Math., 156 (2008), 1499-1509.
doi: 10.1016/j.dam.2005.06.014. |
[5] |
M. El-Khamy, New Approaches to the Analysis and Design of Reed-Solomon Related Codes, Ph.D thesis, California Institute of Technology, 2007. |
[6] |
M. El-Khamy and R. J. McEliece, Bounds on the average binary minimum distance and the maximum likelihood performance of Reed Solomon codes, in 42nd Allerton Conf. Commun. Control Comput., 2004. |
[7] |
M. El-Khamy and R. J. McEliece, The partition weight enumerator of MDS codes and its applications, in Int. Symp. Inf. Theory, 2005, 926-930.
doi: 10.1109/ISIT.2005.1523473. |
[8] |
A. Faldum, J. Lafuente, G. Ochoa and W. Willems, Error probabilities for bounded distance decoding, Des. Codes Crypt., 40 (2006), 237-252.
doi: 10.1007/s10623-006-0010-x. |
[9] |
M. P. C. Fossorier, Critical point for maximum likelihood decoding of linear block codes, IEEE Commun. Letters, 9 (2005), 817-819.
doi: 10.1109/LCOMM.2005.1506713. |
[10] |
J. Han, P. H. Siegel and P. Lee, On the probability of undetected error for overextended Reed-Solomon codes, IEEE Trans. Inf. Theory, 52 (2006), 3662-3669.
doi: 10.1109/ITW.2006.1633800. |
[11] |
T. Kasami and S. Lin, On the probability of undetected error for the maximum distance separable codes, IEEE Trans. Commun., COM-32 (1984), 998-1006.
doi: 10.1109/TCOM.1984.1096175. |
[12] |
J. MacWilliams, A theorem on the distribution of weights in a systematic code, Bell System Tech. J., 42 (1963), 79-94.
doi: 10.1002/j.1538-7305.1963.tb04003.x. |
[13] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North Holland Publishing Co., 1977. |
[14] |
J. Riordan, Combinatorial Identities, Robert E. Krieger Publishing Co., Huntington, New York, 1979. |
[15] |
S. Roman, Coding and Information Theory, Springer-Verlag, New York, 1992. |
[16] |
W. A. Stein et al., Sage Mathematics Software (Version 5.9), The Sage Development Team, 2012, available at http://www.sagemath.org |
[17] |
D. Torrieri, The information-bit error rate for block codes, IEEE Trans. Commun., COM-32 (1984), 474-476.
doi: 10.1109/TCOM.1984.1096082. |
[18] |
D. Torrieri, Information-bit, information-symbol, and decoded-symbol error rates for linear block codes, IEEE Trans. Commun., 36 (1988), 613-617.
doi: 10.1109/26.1477. |
[19] |
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, 2nd edition, Cambridge University Press, 2001.
doi: 10.1017/CBO9780511987045. |
[20] |
K.-P. Yar, D.-S. Yoo and W. Stark, Performance of RS coded $M$-ary modulation with and without symbol overlapping, IEEE Trans. Commun., 56 (2008), 445-453.
doi: 10.1109/TCOMM.2008.050229. |
show all references
References:
[1] |
C. Desset, B. Macq and L. Vandendorpe, Computing the word-, symbol-, and bit-error rates for block error-correcting codes, IEEE Trans. Commun., 52 (2004), 910-921.
doi: 10.1109/TCOMM.2004.829509. |
[2] |
R. Dodunekova and S. M. Dodunekov, Sufficient conditions for good and proper error-detecting codes, IEEE Trans. Inf. Theory, 43 (1997), 2023-2026.
doi: 10.1109/18.641570. |
[3] |
R. Dodunekova and S. M. Dodunekov, The MMD codes are proper for error detection, IEEE Trans. Inf. Theory, 48 (2002), 3109-3111.
doi: 10.1109/TIT.2002.805082. |
[4] |
R. Dodunekova, S. M. Dodunekov and E. Nikolova, A survey on proper codes, Discrete Appl. Math., 156 (2008), 1499-1509.
doi: 10.1016/j.dam.2005.06.014. |
[5] |
M. El-Khamy, New Approaches to the Analysis and Design of Reed-Solomon Related Codes, Ph.D thesis, California Institute of Technology, 2007. |
[6] |
M. El-Khamy and R. J. McEliece, Bounds on the average binary minimum distance and the maximum likelihood performance of Reed Solomon codes, in 42nd Allerton Conf. Commun. Control Comput., 2004. |
[7] |
M. El-Khamy and R. J. McEliece, The partition weight enumerator of MDS codes and its applications, in Int. Symp. Inf. Theory, 2005, 926-930.
doi: 10.1109/ISIT.2005.1523473. |
[8] |
A. Faldum, J. Lafuente, G. Ochoa and W. Willems, Error probabilities for bounded distance decoding, Des. Codes Crypt., 40 (2006), 237-252.
doi: 10.1007/s10623-006-0010-x. |
[9] |
M. P. C. Fossorier, Critical point for maximum likelihood decoding of linear block codes, IEEE Commun. Letters, 9 (2005), 817-819.
doi: 10.1109/LCOMM.2005.1506713. |
[10] |
J. Han, P. H. Siegel and P. Lee, On the probability of undetected error for overextended Reed-Solomon codes, IEEE Trans. Inf. Theory, 52 (2006), 3662-3669.
doi: 10.1109/ITW.2006.1633800. |
[11] |
T. Kasami and S. Lin, On the probability of undetected error for the maximum distance separable codes, IEEE Trans. Commun., COM-32 (1984), 998-1006.
doi: 10.1109/TCOM.1984.1096175. |
[12] |
J. MacWilliams, A theorem on the distribution of weights in a systematic code, Bell System Tech. J., 42 (1963), 79-94.
doi: 10.1002/j.1538-7305.1963.tb04003.x. |
[13] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North Holland Publishing Co., 1977. |
[14] |
J. Riordan, Combinatorial Identities, Robert E. Krieger Publishing Co., Huntington, New York, 1979. |
[15] |
S. Roman, Coding and Information Theory, Springer-Verlag, New York, 1992. |
[16] |
W. A. Stein et al., Sage Mathematics Software (Version 5.9), The Sage Development Team, 2012, available at http://www.sagemath.org |
[17] |
D. Torrieri, The information-bit error rate for block codes, IEEE Trans. Commun., COM-32 (1984), 474-476.
doi: 10.1109/TCOM.1984.1096082. |
[18] |
D. Torrieri, Information-bit, information-symbol, and decoded-symbol error rates for linear block codes, IEEE Trans. Commun., 36 (1988), 613-617.
doi: 10.1109/26.1477. |
[19] |
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, 2nd edition, Cambridge University Press, 2001.
doi: 10.1017/CBO9780511987045. |
[20] |
K.-P. Yar, D.-S. Yoo and W. Stark, Performance of RS coded $M$-ary modulation with and without symbol overlapping, IEEE Trans. Commun., 56 (2008), 445-453.
doi: 10.1109/TCOMM.2008.050229. |
[1] |
Andrew Klapper, Andrew Mertz. The two covering radius of the two error correcting BCH code. Advances in Mathematics of Communications, 2009, 3 (1) : 83-95. doi: 10.3934/amc.2009.3.83 |
[2] |
Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889 |
[3] |
Sanghoon Kwon, Seonhee Lim. Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 169-186. doi: 10.3934/dcds.2018008 |
[4] |
Marcelo Muniz S. Alves, Luciano Panek, Marcelo Firer. Error-block codes and poset metrics. Advances in Mathematics of Communications, 2008, 2 (1) : 95-111. doi: 10.3934/amc.2008.2.95 |
[5] |
Yanyan Gao, Qin Yue, Xinmei Huang, Yun Yang. Two classes of cyclic extended double-error-correcting Goppa codes. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022003 |
[6] |
Muhammad Ajmal, Xiande Zhang. New optimal error-correcting codes for crosstalk avoidance in on-chip data buses. Advances in Mathematics of Communications, 2021, 15 (3) : 487-506. doi: 10.3934/amc.2020078 |
[7] |
René B. Christensen, Carlos Munuera, Francisco R. F. Pereira, Diego Ruano. An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2021072 |
[8] |
Ben A. Vanderlei, Matthew M. Hopkins, Lisa J. Fauci. Error estimation for immersed interface solutions. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1185-1203. doi: 10.3934/dcdsb.2012.17.1185 |
[9] |
Rua Murray. Approximation error for invariant density calculations. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 535-557. doi: 10.3934/dcds.1998.4.535 |
[10] |
El Miloud Zaoui, Marc Laforest. Stability and modeling error for the Boltzmann equation. Kinetic and Related Models, 2014, 7 (2) : 401-414. doi: 10.3934/krm.2014.7.401 |
[11] |
Robert S. Strichartz. Average error for spectral asymptotics on surfaces. Communications on Pure and Applied Analysis, 2016, 15 (1) : 9-39. doi: 10.3934/cpaa.2016.15.9 |
[12] |
María Chara, Ricardo A. Podestá, Ricardo Toledano. The conorm code of an AG-code. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021018 |
[13] |
Qichun Wang, Chik How Tan, Pantelimon Stănică. Concatenations of the hidden weighted bit function and their cryptographic properties. Advances in Mathematics of Communications, 2014, 8 (2) : 153-165. doi: 10.3934/amc.2014.8.153 |
[14] |
Yujuan Li, Guizhen Zhu. On the error distance of extended Reed-Solomon codes. Advances in Mathematics of Communications, 2016, 10 (2) : 413-427. doi: 10.3934/amc.2016015 |
[15] |
Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070 |
[16] |
Xiaoying Han, Jinglai Li, Dongbin Xiu. Error analysis for numerical formulation of particle filter. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1337-1354. doi: 10.3934/dcdsb.2015.20.1337 |
[17] |
Xin-He Miao, Jein-Shan Chen. Error bounds for symmetric cone complementarity problems. Numerical Algebra, Control and Optimization, 2013, 3 (4) : 627-641. doi: 10.3934/naco.2013.3.627 |
[18] |
Benedict Geihe, Martin Rumpf. A posteriori error estimates for sequential laminates in shape optimization. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1377-1392. doi: 10.3934/dcdss.2016055 |
[19] |
Anders C. Hansen. A theoretical framework for backward error analysis on manifolds. Journal of Geometric Mechanics, 2011, 3 (1) : 81-111. doi: 10.3934/jgm.2011.3.81 |
[20] |
Ye Sun, Daniel B. Work. Error bounds for Kalman filters on traffic networks. Networks and Heterogeneous Media, 2018, 13 (2) : 261-295. doi: 10.3934/nhm.2018012 |
2021 Impact Factor: 1.015
Tools
Metrics
Other articles
by authors
[Back to Top]