Capacity of the Gaussian Erasure Channel

This paper finds the capacity of linear time-invariant additive Gaussian noise channels observed through a memoryless erasure channel. This problem requires obtaining the asymptotic spectral distribution of a submatrix of a nonnegative definite Toeplitz matrix obtained by retaining each column/row independently and with identical probability. We show that the optimum normalized power spectral density is the waterfilling solution for reduced signal-to-noise ratio.

[1]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[2]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[3]  Antonia Maria Tulino,et al.  Random Matrix Theory and Wireless Communications , 2004, Found. Trends Commun. Inf. Theory.

[4]  D. Julian.  Dependent and gaussian erasure networks , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[5]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[6]  Shlomo Shamai,et al.  The impact of frequency-flat fading on the spectral efficiency of CDMA , 2001, IEEE Trans. Inf. Theory.

[7]  Philippe Loubaton,et al.  MMSE analysis of certain large isometric random precoded systems , 2003, IEEE Trans. Inf. Theory.

[8]  S.N. Diggavi,et al.  Information transmission over a finite buffer channel , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[9]  Shlomo Shamai,et al.  Mutual information and minimum mean-square error in Gaussian channels , 2004, IEEE Transactions on Information Theory.

[10]  Bahram Honary,et al.  Power line communications: state of the art and future trends , 2003, IEEE Commun. Mag..

[11]  R. Olshen.  Asymptotic properties of the periodogram of a discrete stationary process , 1967, Journal of Applied Probability.

[12]  Antonia Maria Tulino,et al.  Capacity-achieving input covariance for single-user multi-antenna channels , 2006, IEEE Transactions on Wireless Communications.

[13]  Tsachy Weissman,et al.  The Information Lost in Erasures , 2008, IEEE Transactions on Information Theory.

[14]  D. Voiculescu.  Limit laws for Random matrices and free products , 1991 .

[15]  F. Hiai,et al.  The semicircle law, free random variables, and entropy , 2006 .

[16]  Robert M. Gray,et al.  Toeplitz And Circulant Matrices: A Review (Foundations and Trends(R) in Communications and Information Theory) , 2006 .

[17]  Shlomo Shamai,et al.  Fountain Capacity , 2006, IEEE Transactions on Information Theory.

[18]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[19]  John Riordan,et al.  Introduction to Combinatorial Analysis , 1958 .

[20]  J. K. Hunter,et al.  Measure Theory , 2007 .

[21]  John Riordan,et al.  Introduction to Combinatorial Analysis , 1959 .

[22]  P. Spreij.  Probability and Measure , 1996 .

[23]  D. Julian.  Erasure networks , 2002, Proceedings IEEE International Symposium on Information Theory,.

[24]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[25]  Aaron D. Wyner,et al.  Shannon-theoretic approach to a Gaussian cellular multiple-access channel , 1994, IEEE Trans. Inf. Theory.

[26]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[27]  Sergio Verdú,et al.  Spectral efficiency in the wideband regime , 2002, IEEE Trans. Inf. Theory.

[28]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[29]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .