On Communication through a Gaussian Channel with an MMSE Disturbance Constraint

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. The paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length of vector input tends to infinity) expression from the work of Bustin $\textit{et al.}$ The key technical novelty is a new upper bound on the MMSE. This bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values $\textit{below}$ a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). This bound complements the `single-crossing point property' of the MMSE that upper bounds the MMSE for all SNR values $\textit{above}$ a certain value at which the MMSE value is known. The MMSE upper bound provides a refined characterization of the phase-transition phenomenon which manifests, in the limit as the length of the vector input goes to infinity, as a discontinuity of the MMSE for the problem at hand. For vector inputs of size $n=1$, a matching lower bound, to within an additive gap of order $O \left( \log \log \frac{1}{\sf MMSE} \right)$ (where ${\sf MMSE}$ is the disturbance constraint), is shown by means of the mixed inputs technique recently introduced by Dytso $\textit{et al.}$Comment: Submitted to IEEE Transactions on Information Theor

Adaptive and Iterative Multi-Branch MMSE Decision Feedback Detection Algorithms for MIMO Systems

In this work, decision feedback (DF) detection algorithms based on multiple processing branches for multi-input multi-output (MIMO) spatial multiplexing systems are proposed. The proposed detector employs multiple cancellation branches with receive filters that are obtained from a common matrix inverse and achieves a performance close to the maximum likelihood detector (MLD). Constrained minimum mean-squared error (MMSE) receive filters designed with constraints on the shape and magnitude of the feedback filters for the multi-branch MMSE DF (MB-MMSE-DF) receivers are presented. An adaptive implementation of the proposed MB-MMSE-DF detector is developed along with a recursive least squares-type algorithm for estimating the parameters of the receive filters when the channel is time-varying. A soft-output version of the MB-MMSE-DF detector is also proposed as a component of an iterative detection and decoding receiver structure. A computational complexity analysis shows that the MB-MMSE-DF detector does not require a significant additional complexity over the conventional MMSE-DF detector, whereas a diversity analysis discusses the diversity order achieved by the MB-MMSE-DF detector. Simulation results show that the MB-MMSE-DF detector achieves a performance superior to existing suboptimal detectors and close to the MLD, while requiring significantly lower complexity.Comment: 10 figures, 3 tables; IEEE Transactions on Wireless Communications, 201

Using the Oxford cognitive screen to detect cognitive impairment in stroke patients. A comparison with the Mini-Mental State Examination

Background: The Oxford Cognitive Screen (OCS) was recently developed with the aim of describing the cognitive de cits after stroke. The scale consists of 10 tasks encom- passing ve cognitive domains: attention and executive function, language, memory, number processing, and praxis. OCS was devised to be inclusive and un-confounded by aphasia and neglect. As such, it may have a greater potential to be informative on stroke cognitive de cits of widely used instruments, such as the Mini-Mental State Examination (MMSE) or the Montreal Cognitive Assessment, which were originally devised for demented patients. Objective: The present study compared the OCS with the MMSE with regards to their ability to detect cognitive impairments post-stroke. We further aimed to examine perfor- mance on the OCS as a function of subtypes of cerebral infarction and clinical severity. Methods: 325 rst stroke patients were consecutively enrolled in the study over a 9-month period. The OCS and MMSE, as well as the Bamford classi cation and NIHSS, were given according to standard procedures. results: About a third of patients (35.3%) had a performance lower than the cutoff (<22) on the MMSE, whereas 91.6% were impaired in at least one OCS domain, indicating higher incidences of impairment for the OCS. More than 80% of patients showed an impairment in two or more cognitive domains of the OCS. Using the MMSE as a standard of clinical practice, the comparative sensitivity of OCS was 100%. Out of the 208 patients with normal MMSE performance 180 showed impaired performance in at least one domain of the OCS. The discrepancy between OCS and MMSE was particularly strong for patients with milder strokes. As for subtypes of cerebral infarction, fewer patients demonstrated widespread impairments in the OCS in the Posterior Circulation Infarcts category than in the other categories. conclusion: Overall, the results showed a much higher incidence of cognitive impairment with the OCS than with the MMSE and demonstrated no false negatives for OCS vs MMSE. It is concluded that OCS is a sensitive screen tool for cognitive de cits after stroke. In particular, the OCS detects high incidences of stroke-specific cognitive impairments, not detected by the MMSE, demonstrating the importance of cognitive pro ling.Background: The Oxford Cognitive Screen (OCS) was recently developed with the aim of describing the cognitive deficits after stroke. The scale consists of 10 tasks encompassing five cognitive domains: attention and executive function, language, memory, number processing, and praxis. OCS was devised to be inclusive and un-confounded by aphasia and neglect. As such, it may have a greater potential to be informative on stroke cognitive deficits of widely used instruments, such as the Mini-Mental State Examination (MMSE) or the Montreal Cognitive Assessment, which were originally devised for demented patients. Objective: The present study compared the OCS with the MMSE with regards to their ability to detect cognitive impairments post-stroke. We further aimed to examine performance on the OCS as a function of subtypes of cerebral infarction and clinical severity. Methods: 325 first stroke patients were consecutively enrolled in the study over a 9-month period. The OCS and MMSE, as well as the Bamford classification and NIHSS, were given according to standard procedures. Results: About a third of patients (35.3%) had a performance lower than the cutoff(< 22) on the MMSE, whereas 91.6% were impaired in at least one OCS domain, indicating higher incidences of impairment for the OCS. More than 80% of patients showed an impairment in two or more cognitive domains of the OCS. Using the MMSE as a standard of clinical practice, the comparative sensitivity of OCS was 100%. Out of the 208 patients with normal MMSE performance 180 showed impaired performance in at least one domain of the OCS. The discrepancy between OCS and MMSE was particularly strong for patients with milder strokes. As for subtypes of cerebral infarction, fewer patients demonstrated widespread impairments in the OCS in the Posterior Circulation Infarcts category than in the other categories. Conclusion: Overall, the results showed a much higher incidence of cognitive impairment with the OCS than with the MMSE and demonstrated no false negatives for OCS vs MMSE. It is concluded that OCS is a sensitive screen tool for cognitive deficits after stroke. In particular, the OCS detects high incidences of stroke-specific cognitive impairments, not detected by the MMSE, demonstrating the importance of cognitive profiling. © 2018 Mancuso, Demeyere, Abbruzzese, Damora, Varalta, Pirrotta, Antonucci, Matano, Caputo, Caruso, Pontiggia, Coccia, Ciancarelli, Zoccolotti and The Italian OCS Grou

A genetic algorithm-assisted semi-adaptive MMSE multi-user detection for MC-CDMA mobile communication systems

In this work, a novel Minimum-Mean Squared-Error (MMSE) multi-user detector is proposed for MC-CDMA transmission systems working over mobile radio channels characterized by time-varying multipath fading. The proposed MUD algorithm is based on a Genetic Algorithm (GA)-assisted per-carrier MMSE criterion. The GA block works in two successive steps: a training-aided step aimed at computing the optimal receiver weights using a very short training sequence, and a decision-directed step aimed at dynamically updating the weights vector during a channel coherence period. Numerical results evidenced BER performances almost coincident with ones yielded by ideal MMSE-MUD based on the perfect knowledge of channel impulse response. The proposed GA-assisted MMSE-MUD clearly outperforms state-of-the-art adaptive MMSE receivers based on deterministic gradient algorithms, especially for high number of transmitting users

Privacy-Aware MMSE Estimation

We investigate the problem of the predictability of random variable $Y$ under a privacy constraint dictated by random variable $X$, correlated with $Y$, where both predictability and privacy are assessed in terms of the minimum mean-squared error (MMSE). Given that $X$ and $Y$ are connected via a binary-input symmetric-output (BISO) channel, we derive the \emph{optimal} random mapping $P_{Z|Y}$ such that the MMSE of $Y$ given $Z$ is minimized while the MMSE of $X$ given $Z$ is greater than $(1-\epsilon)\mathsf{var}(X)$ for a given $\epsilon\geq 0$. We also consider the case where $(X,Y)$ are continuous and $P_{Z|Y}$ is restricted to be an additive noise channel.Comment: 9 pages, 3 figure

MMSE Optimal Algebraic Space-Time Codes

Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.Comment: 5 pages, 1 figure, journal version to appear in IEEE Transactions on Wireless Communications. Conference version appeared in NCC 2007, IIT Kanpur, Indi

Mutual Information and Minimum Mean-square Error in Gaussian Channels

This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR