This paper finds the capacity of linear timeinvariant systems observed in additive Gaussian noise 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, where the gap to the actual signal-to-noise ratio depends on both the erasure probability and the channel transfer function.We find asymptotic expressions for the capacity in the sporadic erasure and sporadic non-erasure regimes as well as the low and high signal-to-noise regimes.
The Gaussian Erasure Channel / Tulino, ANTONIA MARIA; S., Verdu; G., Caire; S., Shamai. - ELETTRONICO. - (2007), pp. 1-6. (Intervento presentato al convegno 2007 IEEE International Symposium on Information Theory (ISIT2007) tenutosi a Nice, France. nel June 24–29, 2007).
The Gaussian Erasure Channel
TULINO, ANTONIA MARIA;
2007
Abstract
This paper finds the capacity of linear timeinvariant systems observed in additive Gaussian noise 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, where the gap to the actual signal-to-noise ratio depends on both the erasure probability and the channel transfer function.We find asymptotic expressions for the capacity in the sporadic erasure and sporadic non-erasure regimes as well as the low and high signal-to-noise regimes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.