Error detection/correction and fault detection/recovery – Pulse or data error handling – Digital data error correction
Reexamination Certificate
2011-02-15
2011-02-15
Torres, Joseph D (Department: 2112)
Error detection/correction and fault detection/recovery
Pulse or data error handling
Digital data error correction
Reexamination Certificate
active
07890842
ABSTRACT:
A computer-implemented method for correcting transmission errors. According to the method, a transmitted vector corrupted by error can be recovered solving a linear program. The method has applications in the transmission of Internet media, Internet telephony, and speech transmission. In addition, error correction is embedded as a key building block in numerous algorithms, and data-structures, where corruption is possible; corruption of digital data stored on a hard-drive, CD, DVD or similar media is a good example. In short, progress in error correction has potential to impact several storage and communication systems.
REFERENCES:
patent: 4633471 (1986-12-01), Perera et al.
patent: 4763331 (1988-08-01), Matsumoto
patent: 6366941 (2002-04-01), Wolf et al.
patent: 6728295 (2004-04-01), Nallanathan et al.
patent: 7003713 (2006-02-01), Rodgers
patent: 7092451 (2006-08-01), Andrews
patent: 7257170 (2007-08-01), Love et al.
Chase, D.; Class of algorithms for decoding block codes with channel measurement information, IEEE Transactions on Information Theory, vol. 18, Issue 1, Jan. 1972 pp. 170-182.
S. Boyd, and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
Z. D. Bai, Y. Q. Yin, “Limit of the Smallest Eigenvalue of a Large Dimensional Sample Covariance Matrix,”Annals of Probability, vol. 21, No. 3 (Jul. 1993), pp. 1275-1294.
Bruckstein, A.M., Elad, M., “A generalized uncertainty principle and sparse representation in pairs of RNbases,”IEEEE Transactions on Information Theory, 48, pp. 2558-2567 (2002).
Candes, E.J., et al., “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information”, To appear on IEEE Transactions on Information Theory, Available at http://arvix.org/abs/math.NA/0409186, Feb. 2006.
Candes, E.J., Tao, T., “Near Optimal signal recovery from random projectionsand universal encoding strategies” submitted to IEEE Transactions on Information Theory, Oct. 2004, available at http://arvix.org/abs/math.CA/0410542.
Candes, E.J., Romberg, J., “Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions,” To appear in Foundations of Computational Mathematics, Nov. 2004, available at http://arvix.org/abs/math.CA/0411273.
Chen, S.S, Basis Pursuit, Stanford Ph. ˜D˜ Thesis (1995).
Chen, S.S., et al., “Atomic decomposition by basis pursuit,”Society for Industrial and Applied Mathematics Journal of Computing20, pp. 33-61 (1999).
Coifman, F., et al., “Noiselets,”Applied and Computational Harmonic Analysis, 10(1):27-44, 2001.
Davidson, K.R., Szarek, S.J., “Local operator theory, random matrices and Banach spaces,” Handool in Banach Spaces, vol. 1, pp. 317-366 (2001).
Donoho, D.L., “For most large underdetermined systems of linear equations the minimal 11-norm solution is also the sparsest solution,” Manuscript, Sep. 2004, available at http://www-stat.stanford.edu/˜donoho/reports.html.
Donoho, D.L., “Compressed Sensing,” Manuscript, Sep. 2004, available at http://www-stat.stanford.edu/˜donoho/reports.html.
Donoho, D.L., Elad, M., “Optimally sparse representation in general (nonorthogonal) dictionaries via 11minimization,” Proc. Natl. Acad. Sci. USA, 100, pp. 2197-2202 (2003).
Donoho, D.L., Huo, X., “Uncertainty Principles and ideal atomic decomposition”IEEE Transactions on Information Theory, 47, pp. 2845-2862 (2001).
El Karoui, N., “Recent results about the largest eigenvalue of random covariance matrices and statistical application,”Acta Physica Polonica B, vol. 36, No. 9,pp. 2681-2697 (2005).
Geman, S., “A limit theorem for the norm of random matrices,”The Annals Probability, vol. 8, No. 2, pp. 252-261 (1980).
Gribonval, R., Nielsen, M., “Sparse representations in unons bases,”IEEE Trasactions on Information Theory, 49, pp. 3320-3325 (2003).
Johnstone, M., “Large covariance matrices,” Third 2004 Wald Lecture, 6th World congress of the Bernoulli society and 67th Annual Meeting of the IMS, Barcelona (Jul. 2004).
Ledoux, M., “The concentration of measure phenomenon,” Mathematical Surveys and Monographs 89, american Mathematical Society (2001).
Marchenko, V.A., Pastur, L.A., “Distribution of eigenvalues in certain sets of random matrices,” Mat. Sb. (N.S.) 72, pp. 407-535 (in Russian) (1967).
Muirhead, R.J., “Aspects of multivariate statistical theory,” Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York (1982).
Natarajan, B.K., “Sparse approximate solutions to linear systems,”Society for Industrial and Applied Mathematics Journal of Computing, vol. 24, pp. 227-234 (1995).
Silverstein, J.W., “The smallest eigenvalue of a large dimensional Wishart matrix,”Annals of Probability, vol. 13, No. 4 pp. 1364-1368 (1985).
Szarek, S.J., “Condition numbers of random matrices,” J. Complexity 7, pp. 131-149 (1991).
Tropp, J.A., “Greed is good: Algorithmic results for sparse approximation,”IEEE Transactions on Information Theory, vol. 50, No. 10, pp. 2231-2242 (Oct. 2004).
Wachter, K.W., “The limiting empirical measure of multiple discriminant ratios,”The Annals of Statistics, vol. 8, No. 5, pp. 937-957 (1980).
Candes Emmanuel
Tao Terence
California Institute of Technology
Steinfl & Bruno LLP
The Regents of the University of California
Torres Joseph D
LandOfFree
Computer-implemented method for correcting transmission... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Computer-implemented method for correcting transmission..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computer-implemented method for correcting transmission... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2625294