Optimal Quantization of TV White Space Regions for a Broadcast Based Geolocation Database

In the current paradigm, TV white space databases communicate the available channels over a reliable Internet connection to the secondary devices. For places where an Internet connection is not available, such as in developing countries, a broadcast based geolocation database can be considered. This geolocation database will broadcast the TV white space (or the primary services protection regions) on rate-constrained digital channel. In this work, the quantization or digital representation of protection regions is considered for rate-constrained broadcast geolocation database. Protection regions should not be declared as white space regions due to the quantization error. In this work, circular and basis based approximations are presented for quantizing the protection regions. In circular approximation, quantization design algorithms are presented to protect the primary from quantization error while minimizing the white space area declared as protected region. An efficient quantizer design algorithm is presented in this case. For basis based approximations, an efficient method to represent the protection regions by an `envelope' is developed. By design this envelope is a sparse approximation, i.e., it has lesser number of non-zero coefficients in the basis when compared to the original protection region. The approximation methods presented in this work are tested using three experimental data-sets.Comment: 8 pages, 12 figures, submitted to IEEE DySPAN (Technology) 201

On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression

We examine the rate-distortion performance and computational complexity of linear transforms for lossy data compression. The goal is to better understand the performance/complexity tradeoffs associated with using the Karhunen-Loeve transform (KLT) and its fast approximations. Since the optimal transform for transform coding is unknown in general, we investigate the performance penalties associated with using the KLT by examining cases where the KLT fails, developing a new transform that corrects the KLT's failures in those examples, and then empirically testing the performance difference between this new transform and the KLT. Experiments demonstrate that while the worst KLT can yield transform coding performance at least 3 dB worse than that of alternative block transforms, the performance penalty associated with using the KLT on real data sets seems to be significantly smaller, giving at most 0.5 dB difference in our experiments. The KLT and its fast variations studied here range in complexity requirements from O(n^2) to O(n log n) in coding vectors of dimension n. We empirically investigate the rate-distortion performance tradeoffs associated with traversing this range of options. For example, an algorithm with complexity O(n^3/2) and memory O(n) gives 0.4 dB performance loss relative to the full KLT in our image compression experiment

Distributed Functional Scalar Quantization Simplified

Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We address two limitations of previous works: prohibitively expensive decoder design and a restriction to sources with bounded distributions. We rigorously show that a much simpler decoder has equivalent asymptotic performance as the conditional expectation estimator previously explored, thus reducing decoder design complexity. The simpler decoder has the feature of decoupled communication and computation blocks. Moreover, we extend the DFSQ framework with the simpler decoder to acquire sources with infinite-support distributions such as Gaussian or exponential distributions. Finally, through simulation results we demonstrate that performance at moderate coding rates is well predicted by the asymptotic analysis, and we give new insight on the rate of convergence

Numerical method for impulse control of Piecewise Deterministic Markov Processes

This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying Markov chain defined by the post jump location and inter-arrival time. Convergence results are obtained and more importantly we are able to give a convergence rate of the algorithm. The paper is illustrated by a numerical example.Comment: This work was supported by ARPEGE program of the French National Agency of Research (ANR), project "FAUTOCOES", number ANR-09-SEGI-00