The capacity of the two-user Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi ...but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han-Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.
The degrees-of-freedom of a K -user Gaussian interference channel (GIC) has been defined to be the multiple of (1/2)log 2 P at which the maximum sum of achievable rates grows with increasing power P .... In this paper, we establish that the degrees-of-freedom of three or more user, real, scalar GICs, viewed as a function of the channel coefficients, is discontinuous at points where all of the coefficients are nonzero rational numbers. More specifically, for all K > 2, we find a class of K -user GICs that is dense in the GIC parameter space for which K /2 degrees-of-freedom are exactly achievable, and we show that the degrees-of-freedom for any GIC with nonzero rational coefficients is strictly smaller than K /2. These results are proved using new connections with number theory and additive combinatorics.
Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the ...fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.
Computing optimal half-duplex schedules in Gaussian relay networks is a challenging problem due to the lack of an exact capacity characterization and the large number of transmit-receive ...configurations that must be considered. We approach the problem using a constant-gap capacity approximation based on the cut-set bound with independent encoding at the nodes. We formulate an optimization problem to obtain the cut-set optimal half-duplex schedule and find that it is hard to solve in general. This is because it involves an exponential number of variables, since the number of ways to assign each node to either transmitter or receiver mode is exponential in the number of nodes. We present a general technique that takes advantage of specific structures in the topology of a given network and allows us to reduce the complexity of this problem. In certain classes of network topologies, our approach yields polynomial time algorithms for finding half-duplex schedules that achieve capacity within a constant gap. We use simulations to show running time improvements over alternative methods and compare the performance of various half-duplex scheduling approaches in different SNR regimes.
We present a new outer bound for the general two-user discrete memoryless interference channel (IFC) and use it to establish the capacity region of the binary erasure IFC, whose determination was ...left open in . We also show that there are essentially two deterministic binary IFCs, in addition to the binary erasure IFC, whose capacity regions are not obvious from previous results. We determine the capacity region of one of these and apply the aforementioned general outer bound to obtain the best available bound on the maximum achievable sum-rate for the other. We also show that the new general outer bound is tight for one-sided deterministic IFCs that belong to the class studied by El Gamal and Costa.
Exponential error bounds for the finite-alphabet interference channel (IFC) with two transmitter-receiver pairs, are investigated under the random coding regime. Our focus is on optimum decoding, as ...opposed to heuristic decoding rules that have been used in previous works, like joint typicality decoding, decoding based on interference cancellation, and decoding that considers the interference as additional noise. Indeed, the fact that the actual interfering signal is a codeword and not an independent and identically distributed (i.i.d.) noise process complicates the application of conventional techniques to the performance analysis of the optimum decoder. Using analytical tools rooted in statistical physics, we derive a single-letter expression for error exponents achievable under optimum decoding and demonstrate strict improvement over error exponents obtainable using suboptimal decoding rules, but which are amenable to more conventional analysis.
When data traffic in a wireless network is bursty, small amounts of data sporadically become available for transmission, at times that are unknown at the receivers, and an extra amount of energy must ...be spent at the transmitters to overcome this lack of synchronization between the network nodes. In practice, predefined header sequences are used with the purpose of synchronizing the different network nodes. However, in networks where relays must be used for communication, the overhead required for synchronizing the entire network may be very significant. In this paper, we study the fundamental limits of energy-efficient communication in an asynchronous diamond network with two relays. We formalize the notion of relay synchronization by saying that a relay is synchronized if the conditional entropy of the arrival time of the source message given the received signals at the relay is small. We show that the minimum energy-per-bit for bursty traffic in diamond networks is achieved with a coding scheme where each relay is either synchronized or not used at all. A consequence of this result is the derivation of a lower bound to the minimum energy-per-bit for bursty communication in diamond networks. This bound allows us to show that schemes that perform the tasks of synchronization and communication separately (i.e., with synchronization signals preceding the communication block) can achieve the minimum energy-per-bit to within a constant fraction that ranges from 2 in the synchronous case to 1 in the highly asynchronous regime.
Motivation for reward drives adaptive behaviors, whereas impairment of reward perception and experience (anhedonia) can contribute to psychiatric diseases, including depression and schizophrenia. We ...sought to test the hypothesis that the medial prefrontal cortex (mPFC) controls interactions among specific subcortical regions that govern hedonic responses. By using optogenetic functional magnetic resonance imaging to locally manipulate but globally visualize neural activity in rats, we found that dopamine neuron stimulation drives striatal activity, whereas locally increased mPFC excitability reduces this striatal response and inhibits the behavioral drive for dopaminergic stimulation. This chronic mPFC overactivity also stably suppresses natural reward-motivated behaviors and induces specific new brainwide functional interactions, which predict the degree of anhedonia in individuals. These findings describe a mechanism by which mPFC modulates expression of reward-seeking behavior, by regulating the dynamical interactions between specific distant subcortical regions.
A new communication scheme for Gaussian parallel relay networks based on superposition coding and partial decoding at the relays is presented. Some specific examples are proposed in which two ...codebook layers are superimposed. The first-level codebook is constructed with symbols from a binary or ternary alphabet, while the second-level codebook is composed of codewords chosen with Gaussian symbols. The new communication scheme is a generalization of decode-and-forward, amplify-and-forward, and bursty-amplify-and-forward. The asymptotic low-signal-to-noise-ratio regime is studied using achievable rates and minimum energy-per-bit as performance metrics. It is shown that the new scheme outperforms all previously known schemes for some channels and parameter ranges.
Objective:Despite significant advances in neuroscience and treatment development, no widely accepted biomarkers are available to inform diagnostics or identify preferred treatments for individuals ...with major depressive disorder.Method:In this critical review, the authors examine the extent to which multimodal neuroimaging techniques can identify biomarkers reflecting key pathophysiologic processes in depression and whether such biomarkers may act as predictors, moderators, and mediators of treatment response that might facilitate development of personalized treatments based on a better understanding of these processes.Results:The authors first highlight the most consistent findings from neuroimaging studies using different techniques in depression, including structural and functional abnormalities in two parallel neural circuits: serotonergically modulated implicit emotion regulation circuitry, centered on the amygdala and different regions in the medial prefrontal cortex; and dopaminergically modulated reward neural circuitry, centered on the ventral striatum and medial prefrontal cortex. They then describe key findings from the relatively small number of studies indicating that specific measures of regional function and, to a lesser extent, structure in these neural circuits predict treatment response in depression.Conclusions:Limitations of existing studies include small sample sizes, use of only one neuroimaging modality, and a focus on identifying predictors rather than moderators and mediators of differential treatment response. By addressing these limitations and, most importantly, capitalizing on the benefits of multimodal neuroimaging, future studies can yield moderators and mediators of treatment response in depression to facilitate significant improvements in shorter- and longer-term clinical and functional outcomes.
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