Analog Multiple Descriptions: A Zero-Delay Source-Channel Coding Approach

This paper extends the well-known source coding problem of multiple descriptions, in its general and basic setting, to analog source-channel coding scenarios. Encoding-decoding functions that optimally map between the (possibly continuous valued) source and the channel spaces are numerically derived. The main technical tool is a non-convex optimization method, namely, deterministic annealing, which has recently been successfully used in other mapping optimization problems. The obtained functions exhibit several interesting structural properties, map multiple source intervals to the same interval in the channel space, and consistently outperform the known competing mapping techniques.Comment: Submitted to ICASSP 201

A Deterministic Annealing Approach to Witsenhausen's Counterexample

This paper proposes a numerical method, based on information theoretic ideas, to a class of distributed control problems. As a particular test case, the well-known and numerically "over-mined" problem of decentralized control and implicit communication, commonly referred to as Witsenhausen's counterexample, is considered. The method provides a small improvement over the best numerical result so far for this benchmark problem. The key idea is to randomize the zero-delay mappings. which become "soft", probabilistic mappings to be optimized in a deterministic annealing process, by incorporating a Shannon entropy constraint in the problem formulation. The entropy of the mapping is controlled and gradually lowered to zero to obtain deterministic mappings, while avoiding poor local minima. Proposed method obtains new mappings that shed light on the structure of the optimal solution, as well as achieving a small improvement in total cost over the state of the art in numerical approaches to this problem.Comment: submitted to ISIT'1

A Deterministic Annealing Framework for Global Optimization of Delay-Constrained Communication and Control Strategies

This dissertation is concerned with the problem of global optimization of delay constrained communication and control strategies. Specifically, the objective is to obtain optimal encoder and decoder functions that map between the source space and the channel space, to minimize a given cost functional. The cost surfaces associated with these problems are highly complex and riddled with local minima, rendering gradient descent based methods ineffective. This thesis proposes and develops a powerful non-convex optimization method based on the concept of deterministic annealing (DA) - which is derived from information theoretic principles with analogies to statistical physics, and was successfully employed in several problems including vector quantization, classification and regression. DA has several useful properties including reduced sensitivity to initialization and strong potential to avoid poor local minima. DA-based optimization methods are developed here for the following fundamental communication problems: the Wyner-Ziv setting where only a decoder has access to side information, the distributed setting where independent encoders transmit over independent channels to a central decoder, and analog multiple descriptions setting which is an extension of the well known source coding problem of multiple descriptions. Comparative numerical results are presented, which show strict superiority of the proposed method over gradient descent based optimization methods as well as prior approaches in literature. Detailed analysis of the highly non-trivial structure of obtained mappings is provided. The thesis further studies the related problem of global optimization of controller mappings in decentralized stochastic control problems, including Witsenhausen's celebrated 1968 counter-example. It is well-known that most decentralized control problems do not admit closed-form solutions and require numerical optimization. An optimization method is developed, based on DA, for a class of decentralized stochastic control problems. Comparative numerical results are presented for two test problems that show strict superiority of the proposed method over prior approaches in literature, and analyze the structure of obtained controller functions

Zero-Delay Joint Source-Channel Coding in the Presence of Interference Known at the Encoder

Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel is considered in the presence of an additive Gaussian interference signal. The mean squared error (MSE) distortion is minimized under an average power constraint assuming that the interference signal is known at the transmitter. Optimality of simple linear transmission does not hold in this setting due to the presence of the known interference signal. While the optimal encoder-decoder pair remains an open problem, various non-linear transmission schemes are proposed in this paper. In particular, interference concentration (ICO) and one-dimensional lattice (1DL) strategies, using both uniform and non-uniform quantization of the interference signal, are studied. It is shown that, in contrast to typical scalar quantization of Gaussian sources, a non-uniform quantizer, whose quantization intervals become smaller as we go further from zero, improves the performance. Given that the optimal decoder is the minimum MSE (MMSE) estimator, a necessary condition for the optimality of the encoder is derived, and the numerically optimized encoder (NOE) satisfying this condition is obtained. Based on the numerical results, it is shown that 1DL with nonuniform quantization performs closer (compared to the other schemes) to the numerically optimized encoder while requiring significantly lower complexity

Towards Optimal Application Mapping for Energy-Efficient Many-Core Platforms

Siirretty Doriast