S. Pombra

Bio: S. Pombra is an academic researcher. The author has contributed to research in topics: Gaussian & Additive white Gaussian noise. The author has an hindex of 2, co-authored 2 publications receiving 261 citations.

Gaussian feedback capacity

Abstract: The capacity of time-varying additive Gaussian noise channels with feedback is characterized. Toward this end, an asymptotic equipartition theorem for nonstationary Gaussian processes is proved. Then, with the aid of certain matrix inequalities, it is proved that the feedback capacity C/sub FB/ in bits per transmission and the nonfeedback capacity C satisfy C >

Non white Gaussian multiple access channels with feedback

Abstract: Although feedback does not increase the capacity of an additive white noise Gaussian channel, it enables prediction of the noise for non-white additive Gaussian noise channels and results in an improvement of capacity, but at most by a factor of 2 (Pinsker, Ebert, Pombra, and Cover). Although the capacity of white noise channels cannot be increased by feedback, multiple access white noise channels have a capacity increase due to the cooperation induced by feedback. Thomas has shown that the total capacity (sum of the rates of all the senders) of an m-user Gaussian white noise multiple access channel with feedback is less than twice the total capacity without feedback. The present authors show that this factor of 2 bound holds even when cooperation and prediction are combined, by proving that feedback increases the total capacity of an m-user multiple access channel with non-white additive Gaussian noise by at most a factor of 2. >

Determinant Maximization with Linear Matrix Inequality Constraints

Abstract: The problem of maximizing the determinant of a matrix subject to linear matrix inequalities (LMIs) arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interior-point method, with a simplified analysis of the worst-case complexity and numerical results that indicate that the method is very efficient, both in theory and in practice. Compared to existing specialized algorithms (where they are available), the interior-point method will generally be slower; the advantage is that it handles a much wider variety of problems.

When bode meets shannon: control-oriented feedback communication schemes

Abstract: In this paper, we show a general equivalence between feedback stabilization through an analog communication channel, and a communication scheme based on feedback which is a generalization of that of Schalkwijk and Kailath. We also show that the achievable transmission rate of the scheme is given by the Bode's sensitivity integral formula, which characterizes a fundamental limitation of causal feedback. Therefore, we can now use the many results and design tools from control theory to design feedback communication schemes providing desired communication rates, and to generate lower bounds on the channel feedback capacity. We consider single user Gaussian channels with memory and memory-less multiuser broadcast, multiple access, and interference channels. In all cases, the results we obtain either achieve the feedback capacity, when this is known, recover known best rates, or provide new best achievable rates.

The Capacity of Channels With Feedback

Abstract: In this paper, we introduce a general framework for treating channels with memory and feedback. First, we prove a general feedback channel coding theorem based on Massey's concept of directed information. Second, we present coding results for Markov channels. This requires determining appropriate sufficient statistics at the encoder and decoder. We give a recursive characterization of these sufficient statistics. Third, a dynamic programming framework for computing the capacity of Markov channels is presented. Fourth, it is shown that the average cost optimality equation (ACOE) can be viewed as an implicit single-letter characterization of the capacity. Fifth, scenarios with simple sufficient statistics are described. Sixth, error exponents for channels with feedback are presented.

Fifty years of Shannon theory

Abstract: A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication.

Feedback Capacity of the Gaussian Interference Channel to Within 2 Bits

Abstract: We characterize the capacity region to within 2 bits/s/Hz and the symmetric capacity to within 1 bit/s/Hz for the two-user Gaussian interference channel (IC) with feedback. We develop achievable schemes and derive a new outer bound to arrive at this conclusion. One consequence of the result is that feedback provides multiplicative gain at high signal-to-noise ratio: the gain becomes arbitrarily large for certain channel parameters. This finding is in contrast to point-to-point and multiple-access channels where feedback provides no gain and only bounded additive gain respectively. The result makes use of a linear deterministic model to provide insights into the Gaussian channel. This deterministic model is a special case of the El Gamal-Costa deterministic model and as a side-generalization, we establish the exact feedback capacity region of this general class of deterministic ICs.