| The exploitation of prior knowledge is of great importance in many problems where information processing is applied. In this dissertation, we focus on some of these problems and develop novel techniques to take advantage of this knowledge. The first of these problems is data clustering, where it is crucial to determine the underline stochastic process generating the observed data. In many occasions, it is known that the observed data presents temporal dependencies, but existing techniques do not exploit this prior knowledge. In order to do so, we propose the use of a hidden Markov model that acts as a self-organizing map to exploit temporal dependencies in data clustering. The proposed technique is able to automatically identify the number of clusters contained in the data in an unsupervised manner. It also makes it possible to cluster together sequences that are shifted and scaled versions of each other, a problem that to the best of our knowledge has not been systematically addressed in the literature.;The second problem we study is the removal of interference to achieve high data rates in wireless networking. In traditional decoding schemes, interference is assumed as additive white Gaussian noise (AWGN), even though in many occasions it is in fact correlated with previous available data. However, the exploitation of this prior knowledge has not yet been addressed in the context of multi-hop networks. We propose a framework to mitigate the interference by exploiting the correlation in the decoding process. This is done by interpreting the problem as one of transmission over multiple access channels with a priori information.;We next focus on the design of near-optimum quantum error correction codes based on Calderbank-Shor-Steane (CSS) codes, whose quantum parity-check matrix must satisfy very specific constraints. This prior knowledge has to be utilized in the code design. The starting point is the use of the generator and parity-check matrices of a classical channel code with low-density generator matrix (LDGM code). Then, row operations are performed to achieve the desired quantum rate. The proposed family clearly outperforms existing quantum codes, while allowing greater flexibility and ease of design. Discrete Density Evolution (DDE) is utilized to optimize the proposed codes, which are designed with a specific structure inspired in the parallel concatenation of LDGM codes.;As a by-product of the design of quantum codes, we obtain closed-form expressions to predict the error floor of LDGM codes based in the simplification of the DDE process. These expressions are also developed for the case in which the source has a priori information. |
