Large-System Analysis of Multiuser Detection with an Unknown Number of Users: A High-SNR Approach

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service (specified by error probability).Comment: to appear in IEEE Transactions on Information Theor

A Derivation of the Source-Channel Error Exponent using Non-identical Product Distributions

Abstract-This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight

Asymptotic capacity of static multiuser channels with an unknown number of users

Comunicació presentada al 11th International Symposium on Wireless Personal Multimedia Communications (WPMC '08), celebrat els dies 8, 9, 10 i 11 de setembre de 2008 a Lapland, Finlàndia, i organitzat pel Centre for Wireless Communications i el National Institute of Information and Communications Technology.We examine a multiple-access communication system in which multiuser detection is performed without knowledge of the number of active interferers. Using a statistical-physics approach, we compute the single-user channel capacity and spectral efficiency in the large-system limit.This work was supported by the Spanish Ministry of Education/nand Science under Project TEC2006- 01428/TCM, and by the STREP project No. IST-026905 (MASCOT) within the 6th framework program of the European Commission

Mapping epileptic networks with scalp and invasive EEG: applications to epileptogenic zone localization and seizure prediction

This chapter offers an overview of core topics in epilepsy research from a complex systems perspective, starting from single-node studies up to network theory analysis. In its first part, the chapter reviews the advances in EEG biomarkers for epileptic network mapping in both invasive and scalp EEG, including univariate epileptogenic indexes linear connectivity measures within the multivariate autoregressive model, non-linear correlation measures and graph-theoretical properties. In the second part, the chapter covers some of the initial contributions to characterize network dynamics in epilepsy. Particular attention is paid at the seizure prediction problem, using classic dynamical systems approaches as well as the most recent machine-learning prediction algorithms and network-science studies unraveling signatures of the transition from interictal to ictal activity

Large-system analysis of a CDMA dynamic channel under a Markovian input process

Comunicació presentada al IEEE International Symposium on Information Theory (ISIT '08), celebrat a Toronto (Ontario, Canadà) els dies 6, 7, 8, 9, 10 i 11 de juliol de 2008, organitzat per l'Institute of Electrical and Electronics Engineers (IEEE).We study the minimum mean square error (MMSE) and the multiuser efficiency η of large dynamic multiple access communication systems in which optimal multiuser detection is performed at the receiver as the number and the identities of active users is allowed to change at each transmission time. The system dynamics are ruled by a Markov model describing the evolution of the channel occupancy and a large-system analysis is performed when the number of observations grow large. Starting on the equivalent scalar channel and the fixed-point equation tying multiuser efficiency and MMSE, we extend it to the case of a dynamic channel, and derive lower and upper bounds for the MMSE (and, thus, for η as well) holding true in the limit of large signal–to–noise ratios and increasingly large observation time T.This work was supported by the Spanish Ministry of Education and Science/nunder Project TEC2006- 01428/TCM, and by the STREP project No. IST-/n026905 (MASCOT) within the 6th framework program of the European/nCommission

High-SNR analysis of optimum multiuser detection with an unknown number of users

Comunicació presentada al 2009 IEEE Information Theory Workshop celebrat a Taormina (Itàlia) de l'11 al 16 d'octubre de 2009.We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the fixed-point equation whose solutions yield the multiuser efficiency of the optimal detector. Special attention is paid to the large signal-to-noise ratio, which yields tight closed-form bounds on the minimum mean-squared error. These bounds analytically illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. By identifying the region of computationally feasible solutions, we study the maximum load that the detector can support for a given SNR and quality of service, specified by the multiuser efficiency.The work of Ezio Biglieri was supported by the Project CONSOLIDERINGENIO 2010 CSD2008–00010 “COMONSENS”

Large-system analysis of a CDMA dynamic channel under a Markovian input process

Comunicació presentada al IEEE International Symposium on Information Theory (ISIT '08), celebrat a Toronto (Ontario, Canadà) els dies 6, 7, 8, 9, 10 i 11 de juliol de 2008, organitzat per l'Institute of Electrical and Electronics Engineers (IEEE).We study the minimum mean square error (MMSE) and the multiuser efficiency η of large dynamic multiple access communication systems in which optimal multiuser detection is performed at the receiver as the number and the identities of active users is allowed to change at each transmission time. The system dynamics are ruled by a Markov model describing the evolution of the channel occupancy and a large-system analysis is performed when the number of observations grow large. Starting on the equivalent scalar channel and the fixed-point equation tying multiuser efficiency and MMSE, we extend it to the case of a dynamic channel, and derive lower and upper bounds for the MMSE (and, thus, for η as well) holding true in the limit of large signal–to–noise ratios and increasingly large observation time T.This work was supported by the Spanish Ministry of Education and Science/nunder Project TEC2006- 01428/TCM, and by the STREP project No. IST-/n026905 (MASCOT) within the 6th framework program of the European/nCommission

High-SNR analysis of optimum multiuser detection with an unknown number of users

Comunicació presentada al 2009 IEEE Information Theory Workshop celebrat a Taormina (Itàlia) de l'11 al 16 d'octubre de 2009.We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the fixed-point equation whose solutions yield the multiuser efficiency of the optimal detector. Special attention is paid to the large signal-to-noise ratio, which yields tight closed-form bounds on the minimum mean-squared error. These bounds analytically illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. By identifying the region of computationally feasible solutions, we study the maximum load that the detector can support for a given SNR and quality of service, specified by the multiuser efficiency.The work of Ezio Biglieri was supported by the Project CONSOLIDERINGENIO 2010 CSD2008–00010 “COMONSENS”

Nonparametric test for connectivity detection in multivariate autoregressive networks and application to multiunit activity data

Directed connectivity inference has become a cornerstone in neuroscience to analyze multivariate data from neuroimaging and electrophysiological techniques. Here we propose a nonparametric significance method to test the nonzero values of multivariate autoregressive model to infer interactions in recurrent networks. We use random permutations or circular shifts of the original time series to generate the null-hypothesis distributions. The underlying network model is the same as used in multivariate Granger causality, but our test relies on the autoregressive coefficients instead of error residuals. By means of numerical simulation over multiple network configurations, we show that this method achieves a good control of false positives (type 1 error) and detects existing pairwise connections more accurately than using the standard parametric test for the ratio of error residuals. In practice, our method aims to detect temporal interactions in real neuronal networks with nodes possibly exhibiting redundant activity. As a proof of concept, we apply our method to multiunit activity (MUA) recorded from Utah electrode arrays in a monkey and examine detected interactions between 25 channels. We show that during stimulus presentation our method detects a large number of interactions that cannot be solely explained by the increase in the MUA level.MG acknowledges funding from the Marie Sklodowska-Curie Action (grant H2020-MSCA656547). MG and GD were supported by the Human Brain Project (grant FP7-FET-ICT-604102 and H2020-720270 HBP SGA1). GD and ATC were supported by the European Research Council Advanced Grant DYSTRUCTURE (Grant 295129). AT was supported by the UK Medical Research Council (grant MRC G0700976)

Nonparametric test for connectivity detection in multivariate autoregressive networks and application to multiunit activity data

Directed connectivity inference has become a cornerstone in neuroscience to analyze multivariate data from neuroimaging and electrophysiological techniques. Here we propose a nonparametric significance method to test the nonzero values of multivariate autoregressive model to infer interactions in recurrent networks. We use random permutations or circular shifts of the original time series to generate the null-hypothesis distributions. The underlying network model is the same as used in multivariate Granger causality, but our test relies on the autoregressive coefficients instead of error residuals. By means of numerical simulation over multiple network configurations, we show that this method achieves a good control of false positives (type 1 error) and detects existing pairwise connections more accurately than using the standard parametric test for the ratio of error residuals. In practice, our method aims to detect temporal interactions in real neuronal networks with nodes possibly exhibiting redundant activity. As a proof of concept, we apply our method to multiunit activity (MUA) recorded from Utah electrode arrays in a monkey and examine detected interactions between 25 channels. We show that during stimulus presentation our method detects a large number of interactions that cannot be solely explained by the increase in the MUA level.MG acknowledges funding from the Marie Sklodowska-Curie Action (grant H2020-MSCA656547). MG and GD were supported by the Human Brain Project (grant FP7-FET-ICT-604102 and H2020-720270 HBP SGA1). GD and ATC were supported by the European Research Council Advanced Grant DYSTRUCTURE (Grant 295129). AT was supported by the UK Medical Research Council (grant MRC G0700976)