Error detection/correction and fault detection/recovery – Pulse or data error handling – Digital data error correction
Reexamination Certificate
2004-04-16
2009-12-15
Baderman, Scott T (Department: 2112)
Error detection/correction and fault detection/recovery
Pulse or data error handling
Digital data error correction
C714S794000, C714S752000
Reexamination Certificate
active
07634711
ABSTRACT:
The present invention concerns a method of coding information symbols according to a code defined on a Galois field Fq, where q is an integer greater than 2 and equal to a power of a prime number, and of length n=p(q−1), where p>1. This coding is designed so that there exists a corresponding decoding method, also disclosed by the invention, in which the correction of transmission errors essentially comes down to the correction of errors in p words of length (q−1) coded according to Reed-Solomon. The invention is particularly advantageous when, through a suitable choice of parameters, the code according to the invention is an algebraic geometric code: in this case, it is possible to correct the transmission errors by the method already mentioned and/or by a conventional method which is less economical but has a higher performance.
REFERENCES:
patent: 5684811 (1997-11-01), Doran
patent: 5905739 (1999-05-01), Piret et al.
patent: 6334197 (2001-12-01), Eroz et al.
patent: 6438112 (2002-08-01), Piret et al.
patent: 6445755 (2002-09-01), Chung et al.
patent: 6543021 (2003-04-01), Piret
patent: 6578170 (2003-06-01), Piret et al.
patent: 6578171 (2003-06-01), Braneci et al.
patent: 6638318 (2003-10-01), Piret et al.
patent: 6675348 (2004-01-01), Hammons et al.
patent: 6766489 (2004-07-01), Piret et al.
patent: 7051267 (2006-05-01), Yu et al.
patent: 2002/0099997 (2002-07-01), Piret
patent: 2002/0196862 (2002-12-01), Dill et al.
patent: 2003/0177430 (2003-09-01), Piret
patent: 2003/0188252 (2003-10-01), Kim et al.
patent: 2004/0117719 (2004-06-01), Lehobey et al.
patent: 2004/0194006 (2004-09-01), Piret et al.
patent: 1047215 (2000-10-01), None
R.E. Blahut, “Theory and Practice of Error Control Codes”, Addison Wesley, US, XP002272857, pp. 119-123, Chapter 5.8: “The Binary Golay Code”, May 1984.
R.E. Blahut, “Theory and Practice of Error Control Codes”, Addison Wesley, US XP002272858, pp. 94-96, Chapter 5.1: “Viewing a Code from an Extension Field”, May 1984.
J.H. van Lint, “Algebraic Geometric Codes”, Coding Theory and Design Theory: Coding Theory, pp. 137-162, vol. 21, 1990.
T. Hoholdt et al., “On The Decoding of Algebraic-Gemotric codes”, IEEE Transactions on Information Theory, IEEE Inc., New York, vol. 41, No. 6, pp. 1589-1614, Nov. 1995.
A.N. Skorobogatov et al., “On The Decoding of Algebraic-Geometric Codes”, IEEE Transactions on Information Theory, IEEE Inc., vol. 36, No. 5, pp. 1051-1060, Sep. 1990.
M. A. Shokrollahi et al., “Decoding Algebraic-Geometric Codes Beyond the Error-Correction Bound”, Proceedings of the 30thAnnual ACM Symposium on Theory of Computing. Dallas, TX, May 23-26, 1998. Proceedings of the Annual ACM Symposium on Theory of Computing, New York, NY: ACM, US, May 23, 1998, pp. 241-248, XP000970906.
F. Gui-Liang et al., “A Simple Approach for Constructions of Algebraic-Geometric Codes from Affine Plane Curves”, IEEE Transactions on Information Theory, IEEE, New York, pp. 1003-1012, vol. 40, No. 4, Jul. 1, 1994.
F. Gui-Lang et al., “Simplified Understanding and Efficient Decoding of a Class of Algebraic-Geometric Codes”, IEEE Transactions on Information Theory, vol. 40, No. 4, pp. 981-1002, Jul. 1, 1994.
Chih-Wei Liu, et al., “A Fast Parallel Implementation of Feng-Rao Algorithm With Systolic Array Structure”, Information Theory. 1997 IEEE International Symposium On ULM, p. 379, 1997, ISIT, '97, Jun. 29, 1997, XP 010239895.
Chih-Wei Liu, et. al., “A Systolic Array Implementation of the Feng-Rao Algorithm”, IEEE Transactions on Computers, vol. 48, No. 7, pp. 690-706, Jul. 1999.
Feng G.L. et al., “Improved Geometric Goppa Codes. Part I: Basic Theory”, IEEE Transactions on Information Theory, vol. 41, No. 6, pp. 1678-1693, Nov. 11, 1995.
T. Blackmore, et al., “Bounds on The State Complexity of Geometric Goppa Codes”, ISIT 2000, Sorrento, Italy, p. 170, Jun. 25, 2000, XP010510047.
K. S. Laursen, “The Computational Complexity of Effective Construction of Geometric Goppa Codes”, Information Theory, 1997. Proceedings. 1997 IEEE International Symposium On ULM, p. 380, , ISIT '97, Jun. 29, 1997, XP010239896.
K. Yang, et al., “On The Generalized Hamming Weights for Preparata codes Over Z4” Proceedings of the 1997 IEEE International Symposium on Information Theory, ISIT '97, p. 205, Jun. 29, 1997, XP000950795.
T. Helleseth, et al., “On The Coset Weight Distributions of the Z4-Linear Goethals Codes”, Proceedings, 1998 IEEE International Symposium on Cambridge, MA, ISIT '98, p. 400, Aug. 1998, XP010296813.
T. Helleseth, et al., “The Algebraic Decoding of the Z4-Linear Goethals Code”, IEEE Transactions on Information Theory, pp. 2040-2048, vol. 41, No. 6, Nov. 1995.
T. Helleseth, et al. “New Codes with The Same Weight Distributions as the Goethals Codes and the Delsarte-Goethals codes”, Information Theory, 1995. Proceedings, 1995 IEEE International Symposium on Whistler, BC, Canada, p. 274, Sep. 17, 1995, XP01029266.
Helleseth T. et al. “Codes With The Same Weight Distributions As The Goethals Codes and The Delsarte-Goethals Codes”, Designs, Codes and Cryptography, vol. 9, No. 3, pp. 257-266, 1996.
W. J. Reid III, et al. “Maximum Error Magnitude Decoding of the Golay Y23, 12, 7 Code”, Information Theory, 1998. Proceedings, 1998 IEEE International Symposium on Cambridge, MA, ISIT '98, p. 219, Aug. 16, 1998, XP010297124.
P. Robertson, et al. “A Comparison of Optimal and Sub-Optimal Map Decoding Algorithms Operating in the Log Domain”, Communications—Gateway to Globalization, Proceedings of the Conference on Communications, Seattle, IEEE, vol. 2, pp. 1009-1013, Jun. 18, 1995, XP000533149.
Gui-Liang Feng & T.R.N. Rao, “Decoding Algebraic-Geometric Codes up to the Designed Minimum Distance”, IEEE Transactions on Information Theory, vol. 39, No. 1, pp. 37-45, Jan. 1993.
T. Hoholdt et al., Handbook of Coding Theory, Chapter 10: “Algebraic Geometry Codes”, pp. 871-961, 1998.
H. Stichtenoth, “Algebraic Function Fields and Codes”, Foundations of the Theory of Algebraic Function Fields, Chapter 1, Springer-Verlag, US, pp. 1-29, 1993.
Lehobey Frederic
Piret Philippe
Alphonse Fritz
Baderman Scott T
Canon Kabushiki Kaisha
Fitzpatrick ,Cella, Harper & Scinto
LandOfFree
Information coding by algebraic geometric code offering two... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Information coding by algebraic geometric code offering two..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Information coding by algebraic geometric code offering two... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-4060558