On the capacity achieving covariance matrix for Rician MIMO channels: an asymptotic approach

The capacity-achieving input covariance matrices for coherent block-fading correlated MIMO Rician channels are determined. In this case, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. An approximation of the average mutual information is evaluated in this paper in the asymptotic regime where the number of transmit and receive antennas converge to $+\infty$. New results related to the accuracy of the corresponding large system approximation are provided. An attractive optimization algorithm of this approximation is proposed and we establish that it yields an effective way to compute the capacity achieving covariance matrix for the average mutual information. Finally, numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information, while being much more computationally attractive.Comment: 56 pp. Extended version of the published article in IEEE Inf. Th. (march 2010) with more proof

The Average Mutual Information Profile as a Genomic Signature

Background: Occult organizational structures in DNA sequences may hold the key to understanding functional and evolutionary aspects of the DNA molecule. Such structures can also provide the means for identifying and discriminating organisms using genomic data. Species specific genomic signatures are useful in a variety of contexts such as evolutionary analysis, assembly and classification of genomic sequences from large uncultivated microbial communities and a rapid identification system in health hazard situations. Results: We have analyzed genomic sequences of eukaryotic and prokaryotic chromosomes as well as various subtypes of viruses using an information theoretic framework. We confirm the existence of a species specific average mutual information (AMI) profile. We use these profiles to define a very simple, computationally efficient, alignment free, distance measure that reflects the evolutionary relationships between genomic sequences. We use this distance measure to classify chromosomes according to species of origin, to separate and cluster subtypes of the HIV-1 virus, and classify DNA fragments to species of origin. Conclusion: AMI profiles of DNA sequences prove to be species specific and easy to compute. The structure of AMI profiles are conserved, even in short subsequences of a species\u27 genome, rendering a pervasive signature. This signature can be used to classify relatively short DNA fragments to species of origin

An Algorithm for Computing Average Mutual Information using Probability Distribution Smoothing

There is continuing interest in using Average Mutual Information (AMI) to quantify the pair-wise distance between dataset profiles. Among several algorithms used to find a numerical estimation of AMI, the histogram method is the most common since it provides simplicity and least cost. However, this algorithm is known to underestimate the computed entropies and to overestimate the resulting AMI.  Kernel Density Estimator (KDE)-based algorithms advanced to alleviate such systematic errors rely on bin-level smoothing. In the present work, we propose an alternative algorithm that uses smoothing on the probability distribution level. We consider several smoothing functions, both in the probability space and in its frequency space. An experimental approach is used to investigate the effect of such modification on the computation of both the entropy and the AMI. Results show that, to a significant extent, the present method is able to remove systematic errors in computing entropy and AMI. It is also shown that the present algorithm leads to better reconstruction of multivariate time series when AMI is used in conjunction with their independent components

Two-qubit correlations revisited: average mutual information, relevant (and useful) observables and an application to remote state preparation

Understanding how correlations can be used for quantum communication protocols is a central goal of quantum information science. While many authors have linked global measures of correlations such as entanglement or discord to the performance of specific protocols, in general the latter may require only correlations between specific observables. In this work, we first introduce a general measure of correlations for two-qubit states based on the classical mutual information between local observables. We then discuss the role of the symmetry in the state's correlations distribution and accordingly provide a classification of maximally mixed marginals states (MMMS). We discuss the complementarity relation between correlations and coherence. By focusing on a simple yet paradigmatic example, i.e., the remote state preparation protocol, we introduce a method to systematically define proper protocol-tailored measures of correlations. The method is based on the identification of those correlations that are relevant (useful) for the protocol. The approach allows on one hand to discuss the role of the symmetry of the correlations distribution in determining the efficiency of the protocol, both for MMMS and general two-qubit quantum states, and on the other hand to devise an optimized protocol for non-MMMS that can have a better efficiency with respect to the standard one. The scheme we propose can be extended to other communication protocols and more general bipartite settings. Overall our findings clarify how the key resources in simple communication protocols are the purity of the state used and the symmetry of correlations distribution.Comment: Revised Figures, improved notation and clearer text to better highlight the main finding

Use of Average Mutual Information and Derived Measures to Find Coding Regions

One of the important steps in the annotation of genomes is the identification of regions in the genome which code for proteins. One of the tools used by most annotation approaches is the use of signals extracted from genomic regions that can be used to identify whether the region is a protein coding region. Motivated by the fact that these regions are information bearing structures we propose signals based on measures motivated by the average mutual information for use in this task. We show that these signals can be used to identify coding and noncoding sequences with high accuracy. We also show that these signals are robust across species, phyla, and kingdom and can, therefore, be used in species agnostic genome annotation algorithms for identifying protein coding regions. These in turn could be used for gene identification

A multidimensional scaling analysis of musical sounds based on pseudo phase plane

This paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles the MDS technique is used. The MDS is calculated based on two alternative metrics obtained from the PPP, namely, the average mutual information and the fractal dimension. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical sounds