Jan Østergaard

Packetized Predictive Control of Stochastic Systems Over Bit-Rate Limited Channels With Packet Loss

We study a control architecture for linear time-invariant plants with random disturbances and where a network is placed between the controller output and the plant input. The network imposes a constraint on the expected bit-rate and is affected by random independent and identically distributed (i.i.d.) dropouts. Dropout-rates and acknowledgments of receipt are not available at the controller side. To achieve robustness with respect to i.i.d. dropouts, the controller transmits data packets containing quantized plant input predictions. These are provided by an appropriate optimal entropy coded dithered lattice vector quantizer. Within this context, we derive stochastic stability results and provide a noise-shaping model of the closed loop system. This model is employed for performance analysis by using rate-distortion theory.

Energy Efficient State Estimation With Wireless Sensors Through the Use of Predictive Power Control and Coding

We study state estimation via wireless sensors over fading channels. Packet loss probabilities depend upon time-varying channel gains, packet lengths and transmission power levels of the sensors. Measurements are coded into packets by using either independent coding or distributed zero-error coding. At the gateway, a time-varying Kalman filter uses the received packets to provide the state estimates. To trade sensor energy expenditure for state estimation accuracy, we develop a predictive control algorithm which, in an online fashion, determines the transmission power levels and codebooks to be used by the sensors. To further conserve sensor energy, the controller is located at the gateway and sends coarsely quantized power increment commands, only whenever deemed necessary. Simulations based on real channel measurements illustrate that the proposed method gives excellent results.

n-channel entropy-constrained multiple-description lattice vector quantization

In this paper, we derive analytical expressions for the central and side quantizers which, under high-resolution assumptions, minimize the expected distortion of a symmetric multiple-description lattice vector quantization (MD-LVQ) system subject to entropy constraints on the side descriptions for given packet-loss probabilities. We consider a special case of the general n-channel symmetric multiple-description problem where only a single parameter controls the redundancy tradeoffs between the central and the side distortions. Previous work on two-channel MD-LVQ showed that the distortions of the side quantizers can be expressed through the normalized second moment of a sphere. We show here that this is also the case for three-channel MD-LVQ. Furthermore, we conjecture that this is true for the general n-channel MD-LVQ. For given source, target rate, and packet-loss probabilities we find the optimal number of descriptions and construct the MD-LVQ system that minimizes the expected distortion. We verify theoretical expressions by numerical simulations and show in a practical setup that significant performance improvements can be achieved over state-of-the-art two-channel MD-LVQ by using three-channel MD-LVQ.

Sparse Packetized Predictive Control for Networked Control Over Erasure Channels

We study feedback control over erasure channels with packet-dropouts. To achieve robustness with respect to packet-dropouts, the controller transmits data packets containing plant input predictions, which minimize a finite horizon cost function. To reduce the data size of packets, we propose to adopt sparsity-promoting optimizations, namely, l1 - l2 and l2-constrained l0 optimizations, for which efficient algorithms exist. We show how to design the tuning parameters to ensure (practical) stability of the resulting feedback control systems when the number of consecutive packet-dropouts is bounded.

A Framework for Control System Design Subject to Average Data-Rate Constraints

This paper studies discrete-time control systems subject to average data-rate limits. We focus on a situation where a noisy linear system has been designed assuming transparent feedback and, due to implementation constraints, a source-coding scheme (with unity signal transfer function) has to be deployed in the feedback path. For this situation, and by focusing on a class of source-coding schemes built around entropy coded dithered quantizers, we develop a framework to deal with average data-rate constraints in a tractable manner that combines ideas from both information and control theories. As an illustration of the uses of our framework, we apply it to study the interplay between stability and average data-rates in the considered architecture. It is shown that the proposed class of coding schemes can achieve mean square stability at average data-rates that are, at most, 1.254 bits per sample away from the absolute minimum rate for stability established by Nair and Evans. This rate penalty is compensated by the simplicity of our approach.

Design and Analysis of LT Codes with Decreasing Ripple Size

In this paper we propose a new design of LT codes, which decreases the amount of necessary overhead in comparison to existing designs. The design focuses on a parameter of the LT decoding process called the ripple size. This parameter was also a key element in the design proposed in the original work by Luby. Specifically, Luby argued that an LT code should provide a constant ripple size during decoding. In this work we show that the ripple size should decrease during decoding, in order to reduce the necessary overhead. Initially we motivate this claim by analytical results related to the redundancy within an LT code. We then propose a new design procedure, which can provide any desired achievable decreasing ripple size. The new design procedure is evaluated and compared to the current state of the art through simulations. This reveals a significant increase in performance with respect to both average overhead and error probability at any fixed overhead.

Multiple-Description Coding by Dithered Delta–Sigma Quantization

We address the connection between the multiple-description (MD) problem and delta-sigma quantization. The inherent redundancy due to oversampling in delta-sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise-shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically, as the dimension of the lattice vector quantizer and order of the noise-shaping filter approach infinity, the entropy rate of the dithered delta-sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and mean square error (MSE) fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise-shaping filter must be minimum phase and have a piecewise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.

On compressed sensing and its application to speech and audio signals

In this paper, we consider the application of compressed sensing (aka compressive sampling) to speech and audio signals. We discuss the design considerations and issues that must be addressed in doing so, and we apply compressed sensing as a pre-processor to sparse decompositions of real speech and audio signals using dictionaries composed of windowed complex sinusoids. Our results demonstrate that the principles of compressed sensing can be applied to sparse decompositions of speech and audio signals and that it offers a significant reduction of the computational complexity, but also that such signals may pose a challenge due to their non-stationary and complex nature with varying levels of sparsity.

Sequential Error Concealment for Video/Images by Sparse Linear Prediction

In this paper, we propose a novel sequential error concealment algorithm for video and images based on sparse linear prediction. Block-based coding schemes in packet loss environments are considered. Images are modelled by means of linear prediction, and missing macroblocks are sequentially reconstructed using the available groups of pixels. The optimal predictor coefficients are computed by applying a missing data regression imputation procedure with a sparsity constraint. Moreover, an efficient procedure for the computation of these coefficients based on an exponential approximation is also proposed. Both techniques provide high-quality reconstructions and outperform the state-of-the-art algorithms both in terms of PSNR and MS-SSIM.

Power Control and Coding Formulation for State Estimation With Wireless Sensors

Technological advances made wireless sensors cheap and reliable enough to be brought into industrial use. A major challenge arises from the fact that wireless channels introduce random packet dropouts. Power control and coding are key enabling technologies in wireless communications to ensure efficient communication. In this paper, we examine the role of power control and coding for Kalman filtering over wireless correlated channels. Two estimation architectures are considered; initially, the sensors send their measurements directly to a single gateway (GW). Next, wireless relay nodes provide additional links. The GW decides on the coding scheme and the transmitter power levels of the wireless nodes. The decision process is carried out online and adapts to varying channel conditions to improve the tradeoff between state estimation accuracy and energy expenditure. In combination with predictive power control, we investigate the use of multiple-description coding (MDC), zero-error coding (ZEC), and network coding and provide sufficient conditions for the expectation of the estimation error covariance matrix to be bounded. Numerical results suggest that the proposed method may lead to energy savings of around 50%, when compared with an alternative scheme, wherein transmission power levels and bit-rates are governed by simple logic. In particular, ZEC is preferable at time instances with high channel gains, whereas MDC is superior for time instances with low gains. When channels between the sensors and the GW are in deep fades, network coding improves estimation accuracy significantly without sacrificing energy efficiency.