Robust Causal Transform Coding for LQG Systems with Delay Loss in Communications

A networked controlled system (NCS) in which the plant communicates to the controller over a channel with random delay loss is considered. The channel model is motivated by recent development of tree codes for NCS, which effectively translates an erasure channel to one with random delay. A causal transform coding scheme is presented which exploits the plant state memory for efficient communications (compression) and provides robustness to channel delay loss. In this setting, we analyze the performance of linear quadratic Gaussian (LQG) closed-loop systems and the design of the optimal controller. The design of the transform code for LQG systems is posed as a channel optimized source coding problem of minimizing a weighted mean squared error over the channel. The solution is characterized in two steps of obtaining the optimized causal encoding and decoding transforms and rate allocation across a set of transform coding quantizers. Numerical and simulation results for Gauss-Markov sources and an LQG system demonstrate the effectiveness of the proposed schemes.Comment: 6 pages, 4 figures, American Control Conference, Boston, USA, 201

Performance bounds for LPC spectrum quantization

This paper presents a method for obtaining numerical estimates of high rate vector quantization (VQ) performance suitable for sources for which the pdf is not analytically available. In the pro-posed method, the VQ point density is described from a Gaussian mixture model optimized for the data. Employing this method for LPC spectrum quantization, we obtain high rate expressions for both the average spectral distortion (SD) and the distribution func-tion of the SD. We estimate the minimum bits required for a quan-tizer to obtain an average SD of 1 dB and the outlier statistics for that quantizer. We find that approximately 3 bits can be saved as compared to a 2-split LSF-based vector quantizer. 1

Asymptotic Distribution of the Errors in Scalar and Vector Quantizers

High-rate (or asymptotic) quantization theory has found formulas for the average squared length (more generally, the q-th moment of the length) of the error produced by various scalar and vector quantizers with many quantization points. In contrast, this paper finds an asymptotic formula for the probability density of the length of the error and, in certain special cases, for the probability density of the multidimensional error vector, itself. The latter can be used to analyze the distortion of two-stage vector quantization. The former permits one to learn about the point density and cell shapes of a quantizer from a histogram of quantization error lengths. Histograms of the error lengths in simulations agree well with the derived formulas. Also presented are a number of properties of the error density, including the relationship between the error density, the point density and the cell shapes, the fact that its qth moment equals Bennett's integral (a formula for the average distortio..