Feedback capacity of stationary Gaussian channels

IEEE Transactions on Information Theory

Volumn 56, Issue 1, 2010, Pages 57-85

  Kim, Young Han ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Additive Gaussian noise channel; Autoregressive moving average spectrum; Channel capacity; Feedback; Iterative refinement; Linear coding; Stationary Gaussian process

Indexed keywords

ADDITIVE GAUSSIAN NOISE CHANNELS; AUTOREGRESSIVE MOVING AVERAGE; AUTOREGRESSIVE MOVING-AVERAGE SPECTRUM; ITERATIVE REFINEMENT; LINEAR CODING; STATIONARY GAUSSIAN PROCESS;

ACOUSTIC NOISE; CHANNEL CAPACITY; GAUSSIAN DISTRIBUTION; SPECTRAL DENSITY;

GAUSSIAN NOISE (ELECTRONIC);

EID: 73849126263     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2034816     Document Type: Article

References (80)

1. N. I. Akhiezer, The Classical Moment Problem. New York: Hafner, 1965.
2. J. A. Ball, I. Gohberg, and L. Rodman, Interpolation of Rational Matrix Functions. Basel, Switzerland: Birkhäuser Verlag, 1990.
3. A. Böttcher and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices. New York: Springer-Verlag, 1999.
4. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1994.
5. S. Butman, "A general formulation of linear feedback communication systems with solutions," IEEE Trans. Inf. Theory, vol. IT-15, no. 3, pp. 392-400, May 1969.
6. S. Butman, "Linear feedback rate bounds for regressive channels," IEEE Trans. Inf. Theory, vol. IT-22, no. 3, pp. 363-366, May 1976.
7. P. E. Caines, Linear Stochastic Systems. New York: Wiley, 1988.
8. T. M. Cover and S. Pombra, "Gaussian feedback capacity," IEEE Trans. Inf. Theory, vol. IT-35, no. 1, pp. 37-43, Jan. 1989.
9. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York: Wiley, 2006.
10. A. Dembo, "On Gaussian feedback capacity," IEEE Trans. Inf. Theory, vol. 35, no. 5, pp. 1072-1076, Sep. 1989.
11. N. Dunford and J. T. Schwartz, Linear Operators: Part I. General Theory. New York: Wiley, 1958.
12. p Spaces. NewYork: Academic Press, 1970.
13. P. M. Ebert, Error Bounds for Parallel Communication Channels MIT Research Lab. of Electronics, Tech. Rep. 448, 1966.
14. P. M. Ebert, "The capacity of the Gaussian channel with feedback," Bell Syst. Tech. J., vol. 49, pp. 1705-1712, 1970.
15. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. Amsterdam, The Netherlands: North-Holland, 1976.
16. P. Elias, Channel Capacity Without Coding MIT Research Lab. of Electronics, Cambridge, MA, Quarterly Progr. Rep., 1956.
17. P. Elias, "Networks of Gaussian channels with applications to feedback systems," IEEE Trans. Inf. Theory, vol. IT-13, pp. 493-501, 1967.
18. K. Fan, "Fixed-point and minimax theorems in locally convex topological linear spaces," Proc. Nat. Acad. Sci. USA, vol. 38, pp. 121-126, 1952.
19. F. R. Gantmacher, The Theory of Matrices. NewYork: AMS Chelsea, 1959.
20. R. M. Gray, Toeplitz and Circulant Matrices: A Review Information Systems Lab., Stanford University, Stanford, CA, Tech. Rep. 6504-1, 1977.
21. P. E. Green Jr, Feedback Communication Systems, in Lectures on Communication System Theory, E. Baghdady, Ed. New York: McGraw-Hill, 1961, pp. 345-368.
22. U. Grenander and G. Szegö, Toeplitz Forms and Their Applications. Providence, RI: AMS Chelsea, 1958.
23. J. K. Holsinger, Digital Communication Over Fixed Time-continuous Channels with Memory, With Special Application to Telephone Channels MIT Research Lab. of Electronics, Tech. Rep. 430, 1964.
24. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge University Press, 1985.
25. S. Ihara, "Capacity of mismatched Gaussian channels with and without feedback," Probab. Theory Rel. Fields, vol. 84, no. 4, pp. 453-471, 1990.
26. S. Ihara, "On the capacity of the continuous time Gaussian channel with feedback," J. Multivariate Anal., vol. 10, no. 3, pp. 319-331, 1980.
27. S. Ihara, "Capacity of discrete time Gaussian channel with and without feedback-I," Mem. Fac. Sci. Kochi Univ. Ser. A Math., vol. 9, pp. 21-36, 1988.
28. S. Ihara, "Coding theorems for a continuous-time Gaussian channel with feedback," IEEE Trans. Inf. Theory, vol. 40, pp. 2041-2045, Nov. 1994.
29. T. T. Kadota, M. Zakai, and J. Ziv, "Capacity of a continuous memoryless channel with feedback," IEEE Trans. Inf. Theory, vol. 17, pp. 372-378, 1971.
30. T. T. Kadota, "Mutual information of the white Gaussian channel with and without feedback," IEEE Trans. Inf. Theory, vol. IT-17, pp. 368-371, 1971.
31. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
32. T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation. Englewood Cliffs, NJ: Prentice-Hall, 2000.
33. Y.-H. Kim, "Feedback capacity of the first-order moving average Gaussian channel," IEEE Trans. Inf. Theory, vol. IT-52, no. 7, pp. 3063-3079, 2006.
34. Y.-H. Kim, "Gaussian Feedback Capacity," Ph.D. dissertation, Stanford University, Stanford, CA, 2006.
35. Y.-H. Kim, "A coding theorem for a class of stationary channels with feedback," IEEE Trans. Inf. Theory, vol. 54, no. 4, pp. 1488-1499, Apr. 2008.
36. A. N. Kolmogorov, "Stationary sequences in Hilbert space," Bull. Math. Univ. Moscow, vol. 2, no. 6, pp. 1-40, 1941.
37. p Spaces. Cambridge, U.K.: Cambridge University Press, 1980.
38. A. J. Kramer, "Improving communication reliability by use of an intermittent feedback channel," IEEE Trans. Inf. Theory, vol. IT-15, pp. 52-60, Jan. 1969.
39. M. Krein, "On a generalization of some investigations of G. Szegö, V. Smirnoff and A. Kolmogoroff," C. R. (Doklady) Acad. Sci. URSS (N.S.), vol. 46, pp. 91-94, 1945.
40. M. Krein, "On a problem of extrapolation of A. N. Kolmogoroff," C. R. (Doklady) Acad. Sci. URSS (N.S.), vol. 46, pp. 306-309, 1945.
41. P. Lancaster and L. Rodman, Algebraic Riccati Equations. New York: Oxford University Press, 1995.
42. H. J. Landau, "Maximum entropy and the moment problem," Bull. Amer. Math. Soc. (N.S.), vol. 16, no. 1, pp. 47-77, 1987.
43. D. G. Luenberger, Optimization by Vector Space Methods. New York: Wiley, 1969.
44. J. L. Massey, "Causality, feedback, and directed information," in Proc. Int. Symp. Inf. Theory Applicat., Honolulu, HI, Nov. 1990, pp. 303-305.
45. R. E. Megginson, An Introduction to Banach Space Theory. New York: Springer-Verlag, 1998.
46. ∞ Control. Berlin, Germany: Springer-Verlag, 1990.
47. Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1994.
48. N. K. Nikolski, Operators, Functions, and Systems: An Easy Reading. Providence, RI: American Mathematical Society, 2002.
49. J. K. Omura, "Optimum linear transmission of analog data for channels with feedback," IEEE Trans. Inf. Theory, vol. IT-14, pp. 38-43, Jan. 1968.
50. E. Ordentlich, "A class of optimal coding schemes for moving average additive Gaussian noise channels with feedback," in Proc. IEEE Int. Symp. Inf. Theory, Trondheim, Norway, Jun./Jul. 1994, pp. 467-467.
51. L. H. Ozarow, "Random coding for additive Gaussian channels with feedback," IEEE Trans. Inf. Theory, vol. 36, no. 1, pp. 17-22, Jan. 1990.
52. L. H. Ozarow, "Upper bounds on the capacity of Gaussian channels with feedback," IEEE Trans. Inf. Theory, vol. IT-36, no. 1, pp. 156-161, Jan. 1990.
53. J. R. Partington, Interpolation, Identification, and Sampling. New York: Oxford University Press, 1997.
54. J. R. Partington, Linear Operators and Linear Systems: An Analytical Approach to Control Theory. Cambridge, U.K.: Cambridge University Press, 2004.
55. M. S. Pinsker, Information and Information Stability of Random Variables and Processes. San Francisco, CA: Holden-Day, 1964.
56. M. S. Pinsker, "The probability of error in block transmission in a memoryless Gaussian channel with feedback," Problemy Peredǎci Informacii, vol. 4, no. 4, pp. 3-19, 1968.
57. M. S. Pinsker, in Talk Delivered at the Soviet Information Theory Meeting, 1969.
58. W. Rudin, Real and Complex Analysis, 3rd ed. New York: McGraw-Hill, 1987.
59. M. G. Safonov, K. C. Goh, and J. H. Ly, "Control system synthesis via bilinear matrix inequalities," in Proc. Amer. Contr. Conf., Baltimore, MD, Jun. 1994, pp. 45-49.
60. J. P. M. Schalkwijk and T. Kailath, "A coding scheme for additive noise channels with feedback-I: No bandwidth constraint," IEEE Trans. Inf. Theory, vol. IT-12, pp. 172-182, Apr. 1966.
61. J. P. M. Schalkwijk, "A coding scheme for additive noise channels with feedback-II: Band-limited signals," IEEE Trans. Inf. Theory, vol. IT-12, pp. 183-189, Apr. 1966.
62. C. E. Shannon, "Communication in the presence of noise," Proc. IRE, vol. 37, pp. 10-21, 1949.
63. C. E. Shannon, "The zero error capacity of a noisy channel," IRE Trans. Inf. Theory, vol. IT-2, no. 3, pp. 8-19, Sep. 1956.
64. B. Simon, Orthogonal Polynomials on the Unit Circle. Providence, RI: American Mathematical Society, 2005.
65. M. Sion, "On general minimax theorems," Pacific J. Math., vol. 8, pp. 171-176, 1958.
66. G. Szego″, "Ein grenzwertsatzüber die toeplitzschen determinanten einer reellen positive funktion," Math. Ann., vol. 76, no. 4, pp. 490-503, 1915.
67. G. Szego″, "Beiträge zur theorie der toeplitzschen formen," Math. Z., vol. 6, no. 3-4, pp. 167-202, 1920.
68. G. Szego″, "On certain Hermitian forms associated with the Fourier series of a positive function," Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.], vol. 1952, pp. 228-238, 1952.
69. J. C. Tiernan, "Analysis of the optimum linear system for the autoregressive forward channel with noiseless feedback," IEEE Trans. Inf. Theory, vol. IT-22, pp. 359-363, May 1976.
70. J. C. Tiernan and J. P. M. Schalkwijk, "An upper bound to the capacity of the band-limited Gaussian autoregressive channel with noiseless feedback," IEEE Trans. Inf. Theory, vol. IT-20, pp. 311-316, 1974.
71. L. Vandenberghe, S. Boyd, and S.-P. Wu, "Determinant maximization with linear matrix inequality constraints," SIAM J. Matrix Anal. Appl., vol. 19, no. 2, pp. 499-533, 1998.
72. P. Whittle, Risk-Sensitive Optimal Control. Chichester, U.K.: Wiley, 1990.
73. J. Wolfowitz, "Signalling over a Gaussian channel with feedback and autoregressive noise," J. Appl. Probability, vol. 12, no. 4, pp. 713-723, 1975.
74. V. A. Yakubovich, "Nonconvex optimization problem: The infinitehorizon linear-quadratic control problem with quadratic constraints," Syst. Contr. Lett., vol. 19, no. 1, pp. 13-22, 1992.
75. K. Yanagi, H. W. Chen, and J. W. Yu, "Operator inequality and its application to capacity of Gaussian channel," Taiwanese J. Math., vol. 4, no. 3, pp. 407-416, Sep. 2000.
76. S. Yang, "The Capacity of Communication Channels With Memory," Ph.D. dissertation, Harvard University, Cambridge, MA, 2004.
77. S. Yang, A. Kavčić, and S. Tatikonda, "Feedback capacity of finite-state machine channels," IEEE Trans. Inf. Theory, vol. IT-51, no. 3, pp. 799-810, Mar. 2005.
78. S. Yang, "On the Feedback Capacity of Power-constrained Gaussian Noise Channels with Memory," IEEE Trans. Inf. Theory, vol. 53, no. 3, pp. 929-954, Mar. 2007.
79. S. Zahedi, Gaussian Feedback Capacity With Feedback Stanford University, Stanford, CA, EE 392O Class Proj. Rep., 2003.
80. K. S. Zigangirov, "Upper bounds for the probability of error for channels with feedback," Problemy Peredači Informacii, vol. 6, no. 2, pp. 87-92, 1970.