Browsing by Subject "Upper and lower bounds"

Now showing 1 - 5 of 5

Open Access
On the capacity of MIMO systems with amplitude-limited inputs
(IEEE, 2014) Elmoslimany, A.; Duman, Tolga M.
In this paper, we study the capacity of multiple-input multiple-output (MIMO) systems under the constraint that amplitude-limited inputs are employed. We compute the channel capacity for the special case of multiple-input singleo-utput (MISO) channels, while we are only able to provide upper and lower bounds on the capacity of the general MIMO case. The bounds are derived by considering an equivalent channel via singular value decomposition, and by enlarging and reducing the corresponding feasible region of the channel input vector, for the upper and lower bounds, respectively. We analytically characterize the asymptotic behavior of the derived capacity upper and lower bounds for high and low noise levels, and study the gap between them. We further provide several numerical examples illustrating their computation.
Open Access
Sensitivity reduction by stable controllers for mIMO infinite dimensional systems via the tangential nevanlinna-Pick interpolation
(IEEE, 2014) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in C +, but they are allowed to possess infinitely many poles in C +. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method.
Open Access
Tangential Nevanlinna-Pick interpolation for strong stabilization of MIMO distributed parameter systems
(IEEE, 2012-12) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding stable controllers that stabilize a multi-input multi-output distributed parameter system while simultaneously reducing the sensitivity of the system. The plants we consider have finitely many unstable transmission zeros, but they can possess infinitely many unstable poles. Using the tangential Nevanlinna-Pick interpolation with boundary conditions, we obtain both upper and lower bounds of the minimum sensitivity that can be achieved by stable controllers. We also derive a method to find stable controllers for sensitivity reduction. In addition, we apply the proposed method to a repetitive control system. © 2012 IEEE.
Open Access
A unified approach to universal prediction: Generalized upper and lower bounds
(Institute of Electrical and Electronics Engineers Inc., 2015) Vanli, N. D.; Kozat, S. S.
We study sequential prediction of real-valued, arbitrary, and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios, we achieve matching lower and upper bounds, demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result, we also prove that for the worst case scenario, the performance of randomized output algorithms can be achieved by sequential algorithms so that randomized output algorithms do not improve the performance. © 2012 IEEE.
Open Access
An upper bound on the capacity of non-binary deletion channels
(IEEE, 2013) Rahmati, M.; Duman, Tolga M.
We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C2K(d), and the capacity of the binary deletion channel with the same deletion probability, C2(d), that is, C2K(d) ≤ C2(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0. © 2013 IEEE.