Research
Gonzalo Vazquez-Vilar research interests lie in the fields of information theory, communications theory and signal processing. Currently he is working in the field of Shannon theory with focus on finite-length information theory and statistical hypothesis testing. This section describes some of his contribution to the areas of cognitive radio, main topic of his doctoral dissertation, and finite-length information theory, his current research focus.
Hypothesis Testing and Information Theory
In the context of information theory, statistical hypothesis testing has played a crucial role in deriving converse bounds on error probability starting on the well-knwon sphere-packing bound proposed by Shannon, Gallager, and Berlekamp in 1967. Recently the hypothesis-testing method has gained attention to stablish novel accurate lower bounds for finite-length communication problems.
Joint Source-Channel Coding
Implicit in Shannon's source-channel coding theorem is the fact that reliable transmission of a source through a channel can be accomplished by using separate source and channel codes. This means that a concatenation of a (channel-independent) source code followed by a (source-independent) channel code achieves vanishing error probability as the block length goes to infinity, as long as the source entropy is smaller than the channel capacity. However, in the non-asymptotic regime an optimally designed joint source-channel code can perform strictly better than a separate code.
Interference Management in Cognitive Radio Systems
First, using game theoretical tools, we propose a framework for interference management in which certain interaction is allowed between primary and secondary systems under dynamic spectrum access. Secondly, we address the problem of primary user monitoring using novel detection schemes exploiting multiple antennas, wideband processing, and available knowledge on the primary user transmissions. Using the generalized likelihood ratio test (GLRT) for different signal models we study the asymptotic optimality of these and several detectors in the literature.