Convolutive superposition for multicarrier cognitive radio systems

Recently, we proposed a spectrum-sharing paradigm for single-carrier cognitive radio (CR) networks, where a secondary user (SU) is able to maintain or even improve the performance of a primary user (PU) transmission, while also obtaining a low-data rate channel for its own communication. According to such a scheme, a simple multiplication is used to superimpose one SU symbol on a block of multiple PU symbols.The scope of this paper is to extend such a paradigm to a multicarrier CR network, where the PU employs an orthogonal frequency-division multiplexing (OFDM) modulation scheme. To improve its achievable data rate, besides transmitting over the subcarriers unused by the PU, the SU is also allowed to transmit multiple block-precoded symbols in parallel over the OFDM subcarriers used by the primary system. Specifically, the SU convolves its block-precoded symbols with the received PU data in the time-domain, which gives rise to the term convolutive superposition. An information-theoretic analysis of the proposed scheme is developed, which considers different amounts of network state information at the secondary transmitter, as well as different precoding strategies for the SU. Extensive simulations illustrate the merits of our analysis and designs, in comparison with conventional CR schemes, by considering as performance indicators the ergodic capacity of the considered systems.Comment: 29 pages, 8 figure

High-dimensional learning of linear causal networks via inverse covariance estimation

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared l_2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a "gap" between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded.Comment: 41 pages, 7 figure

Techniques for clustering gene expression data

Many clustering techniques have been proposed for the analysis of gene expression data obtained from microarray experiments. However, choice of suitable method(s) for a given experimental dataset is not straightforward. Common approaches do not translate well and fail to take account of the data profile. This review paper surveys state of the art applications which recognises these limitations and implements procedures to overcome them. It provides a framework for the evaluation of clustering in gene expression analyses. The nature of microarray data is discussed briefly. Selected examples are presented for the clustering methods considered

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor