On the capacity of ternary Hebbian networks

Networks of ternary neurons storing random vectors over the set (-1,0,1) by the so-called Hebbian rule are considered. It is shown that the maximal number of stored patterns that are equilibrium states of the network with probability tending to one as N tends to infinity is at least on the order of N/sup 2-1// alpha /K, where N is the number of neurons, K is the number of nonzero elements in a pattern. and t= alpha K, 1/2< alpha <1, is the threshold in the neuron function. While. for small K, this bound is similar to that obtained for fully connected binary networks, the number of interneural connections required in the ternary case is considerably smaller. Similar bounds, incorporating error probabilities, are shown to guarantee, in the same probabilistic sense, the correction of errors in the nonzero elements and in the location of these elements.<>     

On the high-SNR capacity of noncoherent networks

We obtain the first term in the high signal-to-noise ratio (SNR) asymptotic expansion of the sum-rate capacity of noncoherent fading networks, i.e., networks where the transmitters and receivers-while fully cognizant of the fading law-have no access to the fading realization. This term is an integer multiple of log log SNR with the coefficient having a simple combinatorial characterization. It can be interpreted as the effective number of parallel channels that can be supported by the network, i.e., as the maximal number of point-to-point single-user scalar channels that can be supported by the network in a manner that will allow, with proper power allocation, negligible cross interference. The results hold irrespective of whether the transmitters can cooperate or must operate in an multiple-access regime; irrespective of whether feedback from the receivers to the transmitters is available or not; and irrespective of whether the receivers can cooperate or not     

On the teletraffic capacity of CDMA cellular networks

The aim of this paper is to contribute to the understanding of the teletraffic behavior of code-division multiple-access (CDMA) cellular networks. In particular, we examine a technique to assess the reverse link traffic capacity and its sensitivity to various propagation and system parameters. We begin by discussing methods of characterizing interference from other users in the network. These methods are extremely important in the development of the traffic models. We begin with a review of several existing approaches to the problem of handling other-cell interference before presenting a novel characterization of the interference in the form of an analytic expression for the interference distribution function in the deterministic propagation environment. We then look at extending the capacity analyses that assume a fixed and equal number of users in every cell to handle the random nature of call arrivals and departures. The simplest way to do this is by modeling each cell of the network as an independent M/G/x∞ queue. This allows us to replace the deterministic number of users in each cell by an independent Poisson random variable for each cell. The resulting compound Poisson sums have some very nice properties that allow us to calculate an outage probability by analyzing a single random sum. This leads to a very efficient technique for assessing the reverse link traffic capacity of CDMA cellular networks     

On the capacity of large Gaussian relay networks

The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cut-set arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cut-set upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source-channel coding problem, and it is well known that the source-channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance-it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source-destination pair, capacity grows with the logarithm of the number of nodes.     

On the capacity of network coding for random networks

We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, l terminals, and n relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.) /spl sim/X, the maximum flow between the source and the terminals is approximately nE[X] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area.     

On the capacity of multiuser MIMO networks with interference

Maximizing the total mutual information of multiuser multiple-input multiple-output (MIMO) systems with interference is a challenging problem. In this paper, we consider the power control problem of finding the maximum sum of mutual information for a multiuser network with mutually interfered MIMO links. We propose a new and powerful global optimization method using a branch-and-bound (BB) framework, coupled with a novel reformulation-linearization technique (RLT). The proposed BB/RLT guarantees finding a global optimum for multiuser MIMO networks with interference. To reduce the complexity of BB/RLT, we propose a modified BB variable selection strategy to accelerate the convergence process. Numerical examples are also given to demonstrate the efficacy of the proposed solution.     

On the mobility/capacity conversion in wireless networks

Given a quality-of-service constraint, a wireless network has to sacrifice its capacity in order to support an increase in mobility. In other words, the network needs to convert some of its capacity into mobility. We develop an analytical model to evaluate the efficiency of the mobility/capacity conversion processes of several wireless networks. One practical implication of our results is that a network, if designed correctly, should have a free convertibility between the two.     

On the capacity region of wireless ad hoc relay networks

I. Introduction Wireless ad hoc network regarded as a risingnetwork model has been discussed widely. Thestudy of the capacity of wireless ad hoc networkshas received significant attention recently. Guptaand Kumar in Ref.[1] proposed a model for studyingthe capacity of fixed ad hoc networks, where nodesare randomly located but are stationary. They madea somewhat pessimistic conclusion that the trafficrate per Source-to-Destination (S-D) pair will go tozero as the number of nodes per unit are…     

On the capacity of some channels with channel state information

We study the capacity of some channels whose conditional output probability distribution depends on a state process independent of the channel input and where channel state information (CSI) signals are available both at the transmitter (CSIT) and at the receiver (CSIR). When the channel state and the CSI signals are jointly independent and identically distributed (i.i.d.), the channel reduces to a case studied by Shannon (1958). In this case, we show that when the CSIT is a deterministic function of the CSIR, optimal coding is particularly simple. When the state process has memory, we provide a general capacity formula and we give some more restrictive conditions under which the capacity has still a simple single-letter characterization, allowing simple optimal coding. Finally, we turn to the additive white Gaussian noise (AWGN) channel with fading and we provide a generalization of some results about capacity with CSI for this channel. In particular, we show that variable-rate coding (or multiplexing of several codebooks) is not needed to achieve capacity and, even when the CSIT is not perfect, the capacity achieving power allocation is of the waferfilling type     

On the capacity of mobile ad hoc networks with delay constraints

Previous work on ad hoc network capacity has focused primarily on source-destination throughput requirements for different models and transmission scenarios, with an emphasis on delay tolerant applications. In such problems, network capacity enhancement is achieved as a tradeoff with transmission delay. In this paper, the capacity of ad hoc networks supporting delay sensitive traffic is studied. First, a general framework is . proposed for characterizing the interactions between the physical and the network layer in an ad hoc network. Then, CDMA ad hoc networks, in which advanced signal processing techniques such as multiuser detection are relied upon to enhance the user capacity, are analyzed. The network capacity is characterized using a combination of geometric arguments and large scale analysis, for several network scenarios employing matched filters, decorrelators and minimum-mean-square-error receivers. Insight into the network performance for finite systems is also provided by means of simulations. Both analysis and simulations show a significant network capacity gain for ad hoc networks employing multiuser detectors, compared with those using matched filter receivers, as well as very good performance even under tight delay and transmission power requirements.     

On the capacity of MIMO broadcast channels with partial side information

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.     

On capacity of random wireless networks with physical-layer network coding

Throughput capacity of a random wireless network has been studied extensively in the literature. Most existing studies were based on the assumption that each transmission involves only one transmitter in order to avoid interference. However, recent studies on physical-layer network coding (PLNC) have shown that such an assumption can be relaxed to improve throughput performance of a wireless network. In PLNC, signals from different senders can be transmitted to the same receiver in the same channel simultaneously. In this paper, we investigate the impact of PLNC on throughput capacity of a random wireless network. Our study reveals that, although PLNC scheme does not change the scaling law, it can improve throughput capacity by a fixed factor. Specifically, for a one-dimensional network, we observe that PLNC can eliminate the effect of interference in some scenarios. A tighter capacity bound is derived for a two-dimensional network. In addition, we also show achievable lower bounds for random wireless networks with network coding and PLNC.     

Forecasting the capacity of mobile networks

Telecommunication Systems - Energy harvesting (EH) body sensor nodes (BSNs) operate independently in the system and are the emerging solution to multiple replacements of battery operated BSNs....     

On the capacity of a multiple-antenna communication link with channel side information

We investigate the capacity of a system with multiple transmit and receive antennas, assuming that the transmitter and receiver both have access to (possibly defective) channel-state information. Two different special cases of a general system are studied in detail. Our main results are capacity expressions for these cases and a general conclusion that the encoder can be split into separate "space-time coding" and "direction weighting" or "beamforming," without capacity loss. We also present numerical results illustrating the dependence of capacity on the parameters of a quantization scheme providing channel-state information to the transmitter from the receiver. These results have high practical value since the assumptions behind them are closely related to the ones of the closed-loop mode in the UMTS/WCDMA standard.     

On capacity of cognitive radio networks with average interference power constraints

Cognitive radio (CR) has been considered as a promising technology to improve the spectrum utilization. In this paper we analyze the capacity of a CR network with average received interference power constraints. Under the assumptions of uniform node placements and a simple power control scheme, the maximum transmit power of a target CR transmitter is characterized by its cumulative distribution function (CDF). We study two CR scenarios for future applications. The first scenario is called the CR based central access network, which aims at providing broadband access to CR devices. In the second scenario, the so-called CR assisted virtual multiple-input multiple-output (MIMO) network, CR is used to improve the access capability of a cellular system. The uplink ergodic channel capacities of both scenarios are derived and analyzed with an emphasis on understanding the impact of numbers of primary users and CR users on the capacity. Numerical and simulation results suggest that the CR based central access network is more suitable for less-populated rural areas where a relatively low density of primary receivers is expected; while the CR assisted virtual MIMO network performs better in urban environments with a dense population of mobile CR users.     

On the power of uniform power: capacity of wireless networks with bounded resources

The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received much attention in recent years. In this paper, we investigate the question of how much the worst-case performance of uniform and non-uniform power assignments differ under constraints such as a bound on the area where nodes are distributed or restrictions on the maximum power available. We determine the maximum factor by which a non-uniform power assignment can outperform the uniform case in the SINR model. More precisely, we prove that in one-dimensional settings the capacity of a non-uniform assignment exceeds a uniform assignment by at most a factor of \(O(\log L_{\max })\) when the length of the network is \(L_{\max }\). In two-dimensional settings, the uniform assignment is at most a factor of \(O(\log P_{\max })\) worse than the non-uniform assignment if the maximum power is \(P_{\max }\). We provide algorithms that reach this capacity in both cases. These bounds are tight in the sense that previous work gave examples of networks where the lack of power control causes a performance loss in the order of these factors. To complement our theoretical results and to evaluate our algorithms with concrete input networks, we carry out simulations on random wireless networks. The results demonstrate that the link sets generated by the algorithms contain around 20–35 % of all links. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable.     

Traffic capacity of product networks

Switched networks based on the Cartesian product of complete graphs have previously been shown to have a high connectivity, but their traffic capacity has not been considered. This letter gives expressions for traffic capacity and blocking probability from which a preferred routing strategy is deduced.     

Broadcast capacity of wireless networks

We present an upper bound on the broadcast capacity of arbitrary ad hoc wireless networks. The throughput obtainable by each node for broadcasting to-all-of the other nodes in a network consisting of n nodes with- fixed transmission ranges and C bits per second channel capacity is bounded by O(C/n), which is equivalent to the upper bound for per node capacity of a fully connected single-hop network.     

Information-theoretic capacity of multi-receiver networks

We consider multi-receiver networks with diversity reception from an information-theoretic point of view. In particular, we find their capacity and investigate how the frequency spectrum should be allocated to the users. We conclude that efficient transmission schemes cannot be built based on reuse partitioning and therefore advocate a spread spectrum approach. We also show that differences in received power levels can be exploited to advantage in multi-access coding and suggest that diversity reception should play an important role. Finally, we consider a sequence of random networks (to include mobility and fading) and show that a notion of network capacity emerges as a law of large numbers.Research funded by the Commonwealth Scholarship and Fellowship plan.