Source Coding When the Side Information May Be Delayed

For memoryless sources, delayed side information at the decoder does not improve the rate-distortion function. However, this is not the case for more general sources with memory, as demonstrated by a number of works focusing on the special case of (delayed) feedforward. In this paper, a setting is studied in which the encoder is potentially uncertain about the delay with which measurements of the side information are acquired at the decoder. Assuming a hidden Markov model for the sources, at first, a single-letter characterization is given for the set-up where the side information delay is arbitrary and known at the encoder, and the reconstruction at the destination is required to be (near) lossless. Then, with delay equal to zero or one source symbol, a single-letter characterization is given of the rate-distortion region for the case where side information may be delayed or not, unbeknownst to the encoder. The characterization is further extended to allow for additional information to be sent when the side information is not delayed. Finally, examples for binary and Gaussian sources are provided.Comment: revised July 201

Rate-Distortion Theory for Secrecy Systems

Secrecy in communication systems is measured herein by the distortion that an adversary incurs. The transmitter and receiver share secret key, which they use to encrypt communication and ensure distortion at an adversary. A model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver, but also potentially has side information. Specifically, the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver's reconstruction sequence. The main contribution is the characterization of the optimal tradeoff among communication rate, secret key rate, distortion at the adversary, and distortion at the legitimate receiver. It is demonstrated that causal side information at the adversary plays a pivotal role in this tradeoff. It is also shown that measures of secrecy based on normalized equivocation are a special case of the framework.Comment: Update version, to appear in IEEE Transactions on Information Theor

New predictive scheme for the control of LTI systems with input delay and unknown disturbances

International audienceA new predictive scheme is proposed for the control of Linear Time Invariant (LTI) systems with a constant and known delay in the input and unknown disturbances. It has been achieved to include disturbances effect in the prediction even though there are completely unknown. The Artstein reduction is thenrevisited thanks to the computation of this new prediction. An extensive comparison with the standard scheme is presented throughout the article. It is proved that the new scheme leads to feedback controllers that are able to reject perfectly constant disturbances. For time-varying ones, a better attenuation is achieved for a wide range of perturbations and for both linear and nonlinear controllers. A criterion is given to characterize this class of perturbations. Finally, some simulations illustrate the results

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor

Optimal adaptive control of time-delay dynamical systems with known and uncertain dynamics

Delays are found in many industrial pneumatic and hydraulic systems, and as a result, the performance of the overall closed-loop system deteriorates unless they are explicitly accounted. It is also possible that the dynamics of such systems are uncertain. On the other hand, optimal control of time-delay systems in the presence of known and uncertain dynamics by using state and output feedback is of paramount importance. Therefore, in this research, a suite of novel optimal adaptive control (OAC) techniques are undertaken for linear and nonlinear continuous time-delay systems in the presence of uncertain system dynamics using state and/or output feedback. First, the optimal regulation of linear continuous-time systems with state and input delays by utilizing a quadratic cost function over infinite horizon is addressed using state and output feedback. Next, the optimal adaptive regulation is extended to uncertain linear continuous-time systems under a mild assumption that the bounds on system matrices are known. Subsequently, the event-triggered optimal adaptive regulation of partially unknown linear continuous time systems with state-delay is addressed by using integral reinforcement learning (IRL). It is demonstrated that the optimal control policy renders asymptotic stability of the closed-loop system provided the linear time-delayed system is controllable and observable. The proposed event-triggered approach relaxed the need for continuous availability of state vector and proven to be zeno-free. Finally, the OAC using IRL neural network based control of uncertain nonlinear time-delay systems with input and state delays is investigated. An identifier is proposed for nonlinear time-delay systems to approximate the system dynamics and relax the need for the control coefficient matrix in generating the control policy. Lyapunov analysis is utilized to design the optimal adaptive controller, derive parameter/weight tuning law and verify stability of the closed-loop system”--Abstract, page iv

Joint Source-Channel Coding Optimized On End-to-End Distortion for Multimedia Source

In order to achieve high efficiency, multimedia source coding usually relies on the use of predictive coding. While more efficient, source coding based on predictive coding has been considered to be more sensitive to errors during communication. With the current volume and importance of multimedia communication, minimizing the overall distortion during communication over an error-prone channel is critical. In addition, for real-time scenarios, it is necessary to consider additional constraints such as fix and small delay for a given bit rate. To comply with these requirements, we seek an efficient joint source-channel coding scheme. In this work, end-to-end distortion is studied for a first order autoregressive synthetic source that represents a general multimedia traffic. This study reveals that predictive coders achieve the same channel-induced distortion performance as memoryless codecs when applying optimal error concealment. We propose a joint source-channel system based on incremental redundancy that satisfies the fixed delay and error-prone channel constraints and combines DPCM as a source encoder and a rate-compatible punctured convolutional (RCPC) error control codec. To calculate the joint source-channel coding rate allocation that minimizes end-to-end distortion, we develop a Markov Decision Process (MDP) approach for delay constrained feedback Hybrid ARQ, and we use a Dynamic Programming (DP) technique. Our simulation results support the improvement in end-to-end distortion compared to a conventional Forward Error Control (FEC) approach with no feedback