| Analog communications have been replaced by systems working within the digital paradigm in many setups. However, for some applications there is an increasing interest in considering the analog paradigm. One reason for this is that with the growing interest in multiterminal communications, low complexity coding schemes which effectively exploit prior knowledge are required. Another strong motivation lies in the realization that in order to optimally encode signals arising in many practical applications, such as video, biomedicine or geosensing, the encoder design must be tuned to the specific statistical structure of each signal, or what is the same, it must operate based on a prior knowledge about the signal of interest. In many occasions, the exploitation of prior knowledge can be performed better in the analog domain.;With the recent development of Compressed Sensing, a new framework for signal acquisition has been proposed. This new theory provides an effective way of leaping over the classical digital communication setting in which a signal is first sampled at the Nyquist/Shannon rate and then quantized before the encoding process, which operates in a discrete alphabet. Compressed Sensing simplifies the acquisition step by exploiting some prior knowledge about the signal, namely, that it admits a sparse representation in a given basis.;This thesis studies the effect of a more general description of prior knowledge in Compressed Sensing than just the fact that the signal is sparse. We show that additional source statistics can effectively be exploited and that, by doing so, the sparsity constraints can be relaxed. Furthermore, instead of limiting the problem to a sensing scenario, we formulate it as an analog joint source-channel coding scheme, where the measures are transmitted through a noisy channel. Interestingly, we show that many of the design guidelines used in digital joint source-channel codes can be beneficial in Compressed Sensing as well.;In addition to single source scenarios, we also consider distributed schemes in which several correlated signals are independently encoded and are jointly decoded in a central estimation center. We design several algorithms which combine the prior knowledge about each signal with the fact that there is an additional correlation between different signals to be exploited in the recovery. Specifically, two types of scenarios are considered: separated channels between each source and the common receiver and multi-access schemes.;In order to measure the potential benefit of exploiting prior knowledge, we consider multivariate Gaussian sources and quantify the benefit of knowing the source statistics with information theoretic tools. Remarkably, in this case for the multi-access channel our analysis leads to the optimal linear encoder when multivariate Gaussian sources are considered. In addition, for analyzing this gain from a practical perspective, we theoretically study the effect of imperfect statistical knowledge and provide closed form expressions to the performance loss caused by the mismatch. |
