BLIND PERFORMANCE ESTIMATION AND QUANTIZER DESIGN WITH APPLICATIONS TO RELAY NETWORKS

In this thesis, we introduce blind estimators for several performance metrics of Bayesian detectors, we study rate-information-optimal quantization and introduce algorithms for quantizer design in the communications context, and we apply our results to a relay-based cooperative communication scheme. After a discussion of the background material which serves as a basis for this thesis, we study blind performance estimation for Bayesian detectors. We consider simple binary and M -ary hypothesis tests and introduce blind estimators for the conditional and unconditional error probabilities, the minimum mean-square error (MSE), and the mutual information. The proposed blind estimators are shown to be unbiased and consistent. Furthermore, we compare the blind estimators for the error probabilities to the corresponding nonblind estimators and we give conditions under which the blind estimators dominate their respective nonblind counterpart for arbitrary distributions of the data. In particular, we show that the blind estimator for the unconditional error probability always dominates the corresponding nonblind estimator in terms of the MSE. Subsequently, the Cramér-Rao lower bound for bit error probability estimation under maximum a posteriori detection is derived. Moreover, it is shown that an efficient estimator does not exist for this problem. Application examples conclude the discussion of blind performance estimators. We then introduce an approach to quantization that we call rate-information quantization. The main idea of rate-information-optimal quantization is to compress data such that its quantized representation is as informative as possible about another random variable. This random variable is called the relevance variable and it is correlated with the data. The rateinformation approach is well suited for communication problems, which is in contrast to ratedistortion (RD) quantization. We focus on the case where the data and the relevance variable are jointly Gaussian and we derive closed-form expressions for the optimal trade-off between the compression rate and the preserved information about the relevance variable. It is then shown that the optimal rate-information trade-off is achieved by suitable linear preprocessing of the data with subsequent MSE-optimal source coding. This result connects RD theory, the Gaussian information bottleneck, and minimum MSE estimation. Furthermore, we show