Epilepsy is one of the most common neurological disorders affecting about 1% of the world population. For patients with focal seizures that cannot be treated with antiepileptic drugs, the common treatment is a surgical procedure for removal of the seizure onset zone (SOZ). In this work we introduce an algorithm for automatic localization of the seizure onset zone (SOZ) in epileptic patients based on electrocorticography (ECoG) recordings. The proposed algorithm builds upon the hypothesis that the abnormal excessive (or synchronous) neuronal activity in the brain leading to seizures starts in the SOZ and then spreads to other areas in the brain. Thus, when this abnormal activity starts, signals recorded at electrodes close to the SOZ should have a relatively large causal influence on the rest of the recorded signals. The SOZ localization is executed in two steps. First, the algorithm represents the set of electrodes using a directed graph in which nodes correspond to recording electrodes and the edges' weights quantify the pair-wise causal influence between the recorded signals. Then, the algorithm infers the SOZ from the estimated graph using a variant of the PageRank algorithm followed by a novel post-processing phase. Inference results for 19 patients show a close match between the SOZ inferred by the proposed approach and the SOZ estimated by expert neurologists (success rate of 17 out of 19).

We study diversity in one-shot communication over molecular timing channels. In the considered channel model the transmitter simultaneously releases a large number of information particles, where the information is encoded in the time of release. The receiver decodes the information based on the random time of arrival of the information particles. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles. We denote this quantity as the system diversity gain, as it depends both on the number of particles transmitted as well as the receiver detection method. Three types of detectors are considered: the maximum-likelihood (ML) detector, a linear detector, and a detector that is based on the first arrival (FA) among all the transmitted particles. We show that for random propagation characterized by right-sided unimodal densities with zero mode, the FA detector is equivalent to the ML detector, and significantly outperforms the linear detector. Moreover, even for densities with positive mode, the diversity gain achieved by the FA detector is very close to that achieved by the ML detector and much higher than the gain achieved by the linear detector.

In this paper, we study linear encoding for a pair of correlated Gaussian sources transmitted over a two-user Gaussian broadcast channel in the presence of unit-delay noiseless feedback, abbreviated as the GBCF. Each pair of source samples is transmitted using a linear transmission scheme in a finite number of channel uses. We investigate three linear transmission schemes: A scheme based on the Ozarow-Leung (OL) code, a scheme based on the linear quadratic Gaussian (LQG) code of Ardestanizadeh et al., and a novel scheme derived in this paper using a dynamic programming (DP) approach. For the OL and LQG schemes we present lower and upper bounds on the minimal number of channel uses needed to achieve a target mean-square error (MSE) pair. For the LQG scheme in the symmetric setting, we identify the optimal scaling of the sources, which results in a significant improvement of its finite horizon performance, and, in addition, characterize the (exact) minimal number of channel uses required to achieve a target MSE. Finally, for the symmetric setting, we show that for any fixed and finite number of channel uses, the DP scheme achieves an MSE lower than the MSE achieved by either the LQG or the OL schemes.

In this paper, we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) wiretap channels (WTCs) with a finite memory, subject to a per-symbol average power constraint on the MIMO channel input. MIMO channels with finite memory are very common in wireless communications as well as in wireline communications (e.g., in communications over power lines). To derive the secrecy capacity of the Gaussian MIMO WTC with finite memory, we first construct an asymptotically equivalent block-memoryless MIMO WTC, which is then transformed into a set of parallel, independent, memoryless MIMO WTCs in the frequency domain. The secrecy capacity of the Gaussian MIMO WTC with finite memory is obtained as the secrecy capacity of the set of parallel, independent, memoryless MIMO WTCs, and is expressed as maximization over the input covariance matrices in the frequency domain. Finally, we detail two applications of our result: First, we show that the secrecy capacity of the Gaussian scalar WTC with finite memory can be achieved by waterfilling, and obtain a closed-form expression for this secrecy capacity. Then, we use our result to characterize the secrecy capacity of narrowband powerline channels, thereby resolving one of the major open issues for this channel model.

This work studies the impact of time-synchronization in molecular timing (MT) channels by analyzing three different modulation techniques. The first requires transmitter-receiver synchronization and is based on modulating information on the release timing of information particles. The other two are asynchronous and are based on modulating information on the relative time between two consecutive releases of information particles using indistinguishable or distinguishable particles. All modulation schemes result in a system that relate the transmitted and the received signals through an additive noise, which follows a stable distribution. As the common notion of the variance of a signal is not suitable for defining the power of stable distributed signals (due to infinite variance), we derive an expression for the geometric power of a large class of stable distributions, and then use this result to characterize the geometric signal-to-noise ratio (G-SNR) for each of the modulation techniques. In addition, for binary communication, we derive the optimal detection rules for each modulation technique. Numerical evaluations indicate that the bit error rate (BER) is constant for a given G-SNR, and the performance gain obtained by using synchronized communication is significant. Yet, it is also shown that by using two distinguishable particles per bit instead of one, the BER of the asynchronous technique can approach that of the synchronous one.

This work studies communication over diffusionbased molecular timing (DBMT) channels. The transmitter simultaneously releases multiple small information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is represented as an additive noise channel. For a DBMT channel, without flow, this noise follows the Levy distribution. Under this channel model, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is further shown that for any additive noise channel with -stable noise, α <; 1, such as the DBMT channel, a linear receiver is not able to take advantage of the release of multiple information particles. Thus, instead of the common low-complexity linear approach, a new detector, which is based on the first arrival (FA) among all the transmitted particles, is derived. Numerical simulations indicate that for a small to medium number of released particles, the performance of the FA detector is very close to the performance of the ML detector.

This work introduces capacity limits for molecular timing (MT) channels, where information is modulated on the release timing of small information particles, and decoded from the time of arrival at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel, this noise is distributed according to the Lévy distribution. Lower and upper bounds on the capacity of the DBMT channel are derived for the case where the delay associated with the propagation of information particles in the channel is finite. These bounds are also shown to be tight.

This work focuses on the minimum transmission energy required for communicating a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless and causal channel output feedback (GBCF). We study the fundamental limit on the required transmission energy for broadcasting a pair of source samples, such that each source can be reconstructed at its respective receiver to within a target distortion, when the source-channel bandwidth ratio is not restricted. We derive a lower bound and three distinct upper bounds on the minimum required energy. For the upper bounds we analyze three transmission schemes: Two schemes are based on separate source-channel coding, and apply coding over multiple samples of source pairs. The third scheme is based on joint source-channel coding obtained by extending the Ozarow-Leung (OL) transmission scheme, which applies uncoded linear transmission. Numerical simulations show that despite its simplicity, the energy-distortion tradeoff of the OL-based scheme is close to that of the better separation-based scheme, which indicates that the OL scheme is attractive for energy-efficient source transmission over GBCFs.

Abstract We study communications under slowly varying channels, and consider three cases of knowledge of the channel impulse response (CIR): full knowledge, no knowledge, and partial knowledge of the CIR. By partial knowledge, we refer to knowing only either the CIR magnitudes or the CIR phases. It is known that obtaining the exact joint maximum‐likelihood estimate (MLE) of the CFO and the SFO requires a two‐dimensional search. Here, we present a new estimation method which uses the Taylor expansion of the MLE cost function, combined with the best linear unbiased estimator, to obtain a method which does not require such a search. The computational complexity of the new method is evaluated. Numerical simulations demonstrate that the new method approaches the corresponding Cramér‐Rao bound for a wide range of signal‐to‐noise ratios, and has superior performance compared to all other existing methods for approximating the solution for the joint MLE, while maintaining a low computational complexity. Copyright © 2015 John Wiley & Sons, Ltd.

Privacy is a critical issue when communicating over shared mediums. A fundamental model for the information-theoretic analysis of secure communications is the wiretap channel (WTC), which consists of a communicating pair and an eavesdropper. In this work we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) WTCs with finite memory. These channels are very common in wireless communications as well as in wireline communications (e.g., in power line communications). We derive a closed-form expression for the secrecy capacity of the MIMO Gaussian WTC with finite memory via the analysis of an equivalent block-memoryless model, which is transformed into a set of parallel independent memoryless MIMO WTCs. The secrecy capacity is expressed as the maximization over the input covariance matrices in the frequency domain. Finally, we show that for the Gaussian scalar WTC with finite memory, the secrecy capacity can be obtained by waterfilling.

We study the uncoded transmission of a bivariate Gaussian source over a two-user symmetric Gaussian broadcast channel with a unit-delay noiseless feedback (GBCF), assuming that each (uncoded) source sample is transmitted using a finite number of channel uses, and that the transmission scheme is linear. We consider three transmission schemes: The scheme of Ardestanizadeh et al., which is based on linear quadratic Gaussian (LQG) control theory, the scheme of Ozarow and Leung (OL), and a novel scheme derived in this work designed using a dynamic programing (DP) approach. For the LQG scheme we characterize the minimal number of channel uses needed to achieve a specified mean-square error (MSE). For the OL scheme we present lower and upper bounds on the minimal number of channel uses needed to achieve a specified MSE, which become tight when the signal-to-noise ratio approaches zero. Finally, we show that for any fixed and finite number of channel uses, the proposed DP scheme achieves MSE lower than the MSE achieved by either the LQG or the OL schemes.

In this work, we consider linear-feedback schemes for the two-user Gaussian broadcast channel with noiseless feedback. We extend the transmission scheme of [Ozarow and Leung, 1984] by applying estimators with memory instead of the memoryless estimators used by Ozarow and Leung (OL) in their original work. A recursive formulation of the mean square errors achieved by the proposed estimators is provided, along with a proof for the existence of a fixed point. This enables characterizing the achievable rates of the extended scheme. Finally, via numerical simulations it is shown that the extended scheme can improve upon the original OL scheme in terms of achievable rates, as well as achieve a low probability of error after a finite number of channel uses.

This work studies the problem of jointly estimating the carrier frequency offset (CFO) and sampling frequency offset (SFO) in orthogonal frequency-division multiplexing (OFDM) systems. Two scenarios are considered: known channel impulse response (CIR) and unknown CIR. It was shown in previous works that the exact joint maximum-likelihood estimate (MLE) of the CFO and the SFO requires a two-dimensional search. In this work, we present a new estimation method which uses the Taylor expansion of the MLE cost function, combined with the best linear unbiased estimator, to obtain an estimator which does not require such a search. Numerical simulations demonstrate that the new method approaches the corresponding Cramér-Rao bound for a wide range of signal-to-noise ratios, and have superior performance compared to all other existing methods for approximating the joint MLE solution, while maintaining a low computational complexity.

We study the transmission of correlated sources over discrete memoryless (DM) multiple-access-relay channels (MARCs), in which both the relay and the destination have access to side information arbitrarily correlated with the sources. As the optimal transmission scheme is an open problem, in this paper, we propose a new joint source-channel coding scheme based on a novel combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding, and obtain the corresponding sufficient conditions. The proposed coding scheme is based on the decode-and-forward strategy, and utilizes CPM for encoding information simultaneously to the relay and the destination, whereas the cooperation information from the relay is encoded via SW source coding. It is shown that there are cases in which the new scheme strictly outperforms the schemes available in the literature. This is the first instance of a source-channel code that uses CPM for encoding information to two different nodes (relay and destination). In addition to sufficient conditions, we present three different sets of single-letter necessary conditions for reliable transmission of correlated sources over DM MARCs. The newly derived conditions are shown to be at least as tight as the previously known necessary conditions.

The characterization of the optimal joint source-channel coding scheme for transmission of correlated sources over multiple-access-relay channels (MARCs) is an open problem. Here, this problem is studied in the presence of arbitrarily correlated side information at both the relay and the destination. Since each transmitter observes only one of the sources, the admissible joint distributions of the sources and channel inputs must satisfy a Markov relationship which constrains their statistical dependence. This observation is used together with the new data processing inequality derived by [Kang and Ulukus, 2011] to obtain two new sets of single-letter necessary conditions. These new conditions are shown to be at least as tight as the previously known ones, and strictly tighter than the cut-set bound.

We study reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs). In MARCs only the destination is interested in reconstructing the sources, while in MABRCs, both the relay and the destination want to reconstruct them. In addition to arbitrary correlation among the source signals at the users, both the relay and the destination have side information correlated with the source signals. Our objective is to determine whether a given pair of sources can be losslessly transmitted to the destination for a given number of channel symbols per source sample, defined as the source-channel rate. Sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rates are characterized. Since operational separation is generally not optimal for MARCs and MABRCs, sufficient conditions for reliable communication using joint source-channel coding schemes based on a combination of the correlation preserving mapping technique with Slepian-Wolf source coding are also derived. For correlated sources transmitted over fading Gaussian MARCs and MABRCs, we present conditions under which separation (i.e., separate and stand-alone source and channel codes) is optimal. This is the first time optimality of separation is proved for MARCs and MABRCs.

Reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs) is considered. In MARCs, only the destination is interested in a reconstruction of the sources, while in MABRCs, both the relay and the destination want to reconstruct the sources. We allow an arbitrary correlation among the sources at the transmitters, and let both the relay and the destination have side information that are correlated with the sources. Two joint source-channel coding schemes are presented and the corresponding sets of sufficient conditions for reliable communication are derived. The proposed schemes use a combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding: the first scheme uses CPM for encoding information to the relay and SW source coding for encoding information to the destination; while the second scheme uses SW source coding for encoding information to the relay and CPM for encoding information to the destination.