The life cycle for a service provider (SP) to launch a new service or tariff plan often requires months of planning and testing. The SP has traditionally used OSS (Operation support systems) and BSS (Business support systems) which are large, non-standard systems providing life cycle management related to launching new digital services (e.g. internet, voice, SMS, IoT) and tariff plans. These OSS/BSS systems, being multi-vendor and custom implementations, involve significant costs and a timeline of months to a year to roll out the service. This problem worsens with evolving technologies such as 5G. This paper addresses the specific need for faster provisioning of 5G network services and their corresponding tariff/billing plans, thus shortening the duration for launch. To provision the network, a combination of a deep neural network and a large language model (LLM) is proposed in this work to automate the generation of network configurations.

A network service provider (SP) often requires months of planning and testing to launch a new service in the form of a tariff plan. This is because SPs traditionally used operation support systems and business support systems which are large multi-vendor systems with custom implementations that are not easily amenable to launching new digital services such as internet, voice, SMS, IoT. In another detailed work, we have highlighted the challenges and proposed a faster approach to provisioning such services on the network. The method used a deep neural network framework and a large language model to automate the generation of network configurations. In this submission, we propose to demonstrate our solution framework.

We consider a multi-hypothesis testing problem involving a$K$-armed bandit. Each arm’s signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker incurs a delay cost for delay until a decision and a switching cost whenever he switches from one arm to another. His goal is to minimise the overall cost until a decision is reached on the true hypothesis. Of interest are policies that satisfy a given constraint on the probability of false detection. This is a sequential decision making problem where the decision maker gets only a limited view of the true state of nature at each stage, but can control his view by choosing the arm to observe at each stage. An information-theoretic lower bound on the total cost (expected time for a reliable decision plus total switching cost) is first identified, and a variation on a sequential policy based on the generalised likelihood ratio statistic is then studied. Due to the vector exponential family assumption, the signal processing at each stage is simple; the associated conjugate prior distribution on the unknown model parameters enables easy updates of the posterior distribution. The proposed policy, with a suitable threshold for stopping, is shown to satisfy the given constraint on the probability of false detection. Under a continuous selection assumption, the policy is also shown to be asymptotically optimal in terms of the total cost among all policies that satisfy the constraint on the probability of false detection.

Workers on Electronic Manufacturing Service (EMS) assembly lines are exposed to a high degree of occupational stress and fatigue. There is a need for assistive technologies to limit worker stress/fatigue. Electro Dermal Activity (EDA) (Skin Conductance) is a known indicator of a worker’s stress/fatigue level. We propose a novel Electrostatic Discharge (ESD) wrist strap-based EDA sensor. Our sensor seamlessly integrates with the dual-wire grounded ESD wrist strap that EMS operators are mandated to wear. Our approach for EDA measurement is non-intrusive, considering that the operators are accustomed to continuous usage of ESD wrist straps. Besides EDA measurement, our front-end circuit also monitors the integrity of the ESD wrist strap and alerts the wearer in the event of an intermittent or open ground. We present the circuit design and stress-test-based experimental results.

This paper studies the problem of identifying an anomalous arm in a multi-armed bandit when each arm is a finite-state Markov process and the arms are restless. Here, anomaly means that the transition probability matrix (TPM) of one of the arms (the odd arm) is different from the common TPM of each of the non-odd arms. The TPMs are unknown to a decision entity that wishes to find the index of the odd arm as quickly as possible, subject to an upper bound on the error probability. We derive an asymptotic lower bound on the expected time required to find the odd arm index, where the asymptotics is as the error probability vanishes. Further, we devise a policy based on the principle of certainty equivalence, and demonstrate that under a continuous selection assumption and a regularity assumption on the TPMs, the policy achieves the lower bound asymptotically. Our achievability analysis is based on resolving the identifiability problem in the context of a certain countable-state controlled Markov process.

In this paper, we consider a multi-armed bandit in which each arm is a Markov process evolving on a finite state space. The state space is common across the arms, and the arms are independent of each other. The transition probability matrix of one of the arms (the odd arm) is different from the common transition probability matrix of all the other arms. A decision maker, who knows these transition probability matrices, wishes to identify the odd arm as quickly as possible, while keeping the probability of decision error small. To do so, the decision maker collects observations from the arms by pulling the arms in a sequential manner, one at each discrete time instant. However, the decision maker has a trembling hand, and the arm that is actually pulled at any given time differs, with a small probability, from the one he intended to pull. The observation at any given time is the arm that is actually pulled and its current state. The Markov processes of the unobserved arms continue to evolve. This makes the arms restless. For the above setting, we derive the first known asymptotic lower bound on the expected time required to identify the odd arm, where the asymptotics is of vanishing error probability. The continued evolution of each arm adds a new dimension to the problem, leading to a family of Markov decision problems (MDPs) on a countable state space. We then stitch together certain parameterised solutions to these MDPs and obtain a sequence of strategies whose expected times to identify the odd arm come arbitrarily close to the lower bound in the regime of vanishing error probability. Prior works dealt with independent and identically distributed (across time) arms and rested Markov arms, whereas our work deals with restless Markov arms.

We consider a double-auction mechanism, which was recently proposed in the context of rate allocation in mobile data-offloading markets; our mechanism is also applicable to the problem of bandwidth allocation in network slicing markets. Network operators (users) derive benefit from offloading their traffic to third party WiFi or femtocell networks (link-suppliers). Link-suppliers experience costs for the additional capacity that they provide. Users and link-suppliers (collectively referred to as agents) have their pay-offs and cost functions as private knowledge. A network-manager decomposes the problem into a network problem (with surrogate pay-offs and surrogate cost functions) and agent problems (one per agent). The surrogate pay-offs and cost functions are modulated by the agents' bids. Agents' payoffs and costs are then determined by the allocations and prices set by the network-manager. Under this design, so long as the agents do not anticipate the effect of their actions on the prices set by the network-manager (i.e., price-taking agents), a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the sum utility of all agents. However, this design fails when the agents (including the link-supplier) are all strategic (price-anticipating). Specifically, the presence of a strategic link-supplier drives the system to an undesirable equilibrium with zero participation resulting in an efficiency loss of 100%. This is in stark contrast to an earlier setting where the users alone are strategic but the link-supplier is not - the efficiency loss is known to be at most 34%. The paper then proposes the following Stackelberg game modification with asymmetric information structures for link-supplier and users in order to alleviate the efficiency-loss problem: the network-manager first announces the allocation and payment functions; he then invites the link-supplier to announce its bid, following which the users are invited to respond with their bids. The resulting Stackelberg games' efficiency losses can be characterized in terms of the link-supplier's cost function when the users' pay-off functions are linear. Specifically, when the link-supplier's cost function is quadratic, the worst case efficiency loss is 25%. Further, the loss in efficiency improves for polynomial cost functions of higher degree. For non-linear utility functions (e.g., α-fair and log utilities), we demonstrate the efficacy of the proposed mechanism via. a detailed numerical study.

The creation of the NPTEL platform in India has led to a vast population of engineering students getting access to quality online content for Signal Processing. These courses are globally accessible, free of cost, and also provide a means of obtaining certificates of proficiency by taking a proctored examination. Recently, a European Union funded project, MIELES, has supported the activity of creating online courses in the fields related to Signal Processing. This paper presents the details and experiences of creating course content and presents guidelines for prospective content creators.

Consider a multi-armed bandit whose arms are independent Markov processes on a common underlying state space. The transition probability matrix of one of the arms (the odd arm) is different from the common transition probability matrix of all the other arms. The goal is to identify the odd arm as quickly as possible while keeping the probability of decision error small. We study the case of restless Markov observations and identify an asymptotic lower bound on the expected stopping time for a decision with vanishing error probability. We then propose a sequential test and show that the asymptotic behaviour of its expected stopping time comes arbitrarily close to that of the lower bound. Prior works dealt with iid arms and rested Markov arms, whereas our work deals with restless Markov arms.

A multi-armed bandit with finitely many arms is studied when each arm is a homogeneous Markov process on an underlying finite state space. The transition law of one of the arms, referred to as the odd arm, is different from the common transition law of all other arms. A learner, who has no knowledge of the above transition laws, has to devise a sequential test to identify the index of the odd arm as quickly as possible, subject to an upper bound on the probability of error. For this problem, we derive an asymptotic lower bound on the expected stopping time of any sequential test of the learner, where the asymptotics is as the probability of error vanishes. Furthermore, we propose a sequential test, and show that the asymptotic behaviour of its expected stopping time comes arbitrarily close to that of the lower bound. Prior works deal with independent and identically distributed arms, whereas our work deals with Markov arms. Our analysis of the rested Markov setting is a key first step in understanding the difficult case of restless Markov setting, which is still open.

A multi-armed bandit with finitely many arms is studied when each arm is a homogeneous Markov process on an underlying finite state space. The transition law of one of the arms, referred to as the odd arm, is different from the common transition law of all other arms. A learner, who has no knowledge of the above transition laws, has to devise a sequential test to identify the index of the odd arm as quickly as possible, subject to an upper bound on the probability of error. For this problem, we derive an asymptotic lower bound on the expected stopping time of any sequential test of the learner, where the asymptotics is as the probability of error vanishes. Furthermore, we propose a sequential test, and show that the asymptotic behaviour of its expected stopping time comes arbitrarily close to that of the lower bound. Prior works deal with iid arms, whereas our work deals with Markov arms.

We provide a data-driven coverage estimation tech- nique that employs machine-learning based regression ideas for exploiting commonality of antenna-gain and other parameters across measurements made in multiple propagation environ- ments. We then show how readily available geographic information system (GIS) data could be exploited for quick classification of geographic areas into various propagation environments, and how this could enable quick and automated estimation of coverage for faster and more efficient deployment of Internet of Things.

We consider a recently proposed double-auction mechanism for mobile data-offloading. Network operators (users) derive benefit from offloading their traffic to third party WiFi or femtocell network (link-supplier). A link-supplier experiences costs for the additional capacity that he provides. Users and link-supplier (collectively referred to as agents) have their utilities and cost function as private knowledge. A system-designer decomposes the problem into a network problem (with surrogate utilities and surrogate cost functions) and agent problems (one per agent). The surrogate utilities and cost functions are modulated by the agents' bids. Agents' payoffs and costs are then determined by the allocations and prices set by the system designer. So long as the agents do not anticipate the effect of their actions, a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the system utility. This work shows that when the agents are strategic (price-anticipating), the presence of strategic supplying agents drives the system to an undesirable equilibrium with zero participation. This is in stark contrast to the setting when link-suppliers are not strategic where the efficiency loss is at most 34%. The paper then proposes a Stackelberg game modification to alleviate the efficiency loss problem. The system designer first announces the allocation and payment functions. He then invites the supplying agents to announce their bids. He then invites the users to respond to the suppliers' bids. The resulting efficiency loss is characterized in terms of the suppliers' cost functions.

We consider the problem of detecting an odd process among a group of Poisson point processes, all having the same rate except the odd process. The actual rates of the odd and non-odd processes are unknown to the decision maker. We consider a time-slotted sequential detection scenario where, at the beginning of each slot, the decision maker can choose which process to observe during that time slot. We are interested in policies that satisfy a given constraint on the probability of false detection. We propose a variation on a sequential policy based on the generalised likelihood ratio statistic. The policy, via suitable thresholding, can be made to satisfy the given constraint on the probability of false detection. Furthermore, we show that the proposed policy is asymptotically optimal in terms of the conditional expected stopping time among all policies that satisfy the constraint on the probability of false detection. The asymptotic is as the probability of false detection is driven to zero. We apply our results to a particular visual search experiment studied recently by neuroscientists. Our model suggests a neuronal dissimilarity index for the visual search task. The neuronal dissimilarity index, when applied to visual search data from the particular experiment, correlates strongly with the behavioural data. However, the new dissimilarity index performs worse than some previously proposed neuronal dissimilarity indices. We explain why this may be attributed to some experiment conditions.

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to switch OFF dynamically a subset of BSs to minimize energy costs. We consider two types of energy cost: 1) the cost of maintaining a BS in the active state and 2) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach-a Max-Weight algorithm along with a Lyapunov-based stability argument-does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight-based channel scheduler that has fast temporal dynamics. We show that using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to opportunistically switch off a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach - a Max-Weight algorithm along with a Lyapunov-based stability argument - does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

We propose a local message passing algorithm based on Belief Propagation (BP) to detect a small hidden Erdos-Rényi (ER) subgraph embedded in a larger sparse ER random graph in the presence of side-information. We consider side-information in the form of revealed subgraph nodes called cues, some of which may be erroneous. Namely, the revealed nodes may not all belong to the subgraph, and it is not known to the algorithm a priori which cues are correct and which are incorrect. We show that asymptotically as the graph size tends to infinity, the expected fraction of misclassified nodes approaches zero for any positive value of a parameter λ, which represents the effective Signal-to-Noise Ratio of the detection problem. Previous works on subgraph detection using BP without side-information showed that BP fails to recover the subgraph when λ <; 1/e. Our results thus demonstrate the substantial gains in having even a small amount of side-information.

Neuroscientists have recently shown that images that are difficult to find in visual search elicit similar patterns of firing across a population of recorded neurons. The$L^{1}$distance between firing rate vectors associated with two images was strongly correlated with the inverse of decision time in behavior. But why should decision times be correlated with$L^{1}$distance? What is the decision-theoretic basis? In our decision theoretic formulation, we model visual search as an active sequential hypothesis testing problem with switching costs. Our analysis suggests an appropriate neuronal dissimilarity index, which correlates equally strongly with the inverse of decision time as the$L^{1}$distance. We also consider a number of other possibilities, such as the relative entropy (Kullback–Leibler divergence) and the Chernoff entropy of the firing rate distributions. A more stringent test of equality of means, which would have provided a strong backing for our modeling, fails for our proposed as well as the other already discussed dissimilarity indices. However, test statistics from the equality of means test, when used to rank the indices in terms of their ability to explain the observed results, places our proposed dissimilarity index at the top followed by relative entropy, Chernoff entropy, and the$L^{1}$indices. Computations of the different indices require an estimate of the relative entropy between two Poisson point processes. An estimator is developed and is shown to have near unbiased performance for almost all operating regions.

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

To select an appropriate technology for the deployment of an Internet-of-Things (IoT) network inside the Indian Institute of Science (IISc) campus, we first compare available wireless technologies based on their data sheets. After selecting two of the best available sub-GHz devices, we characterize them by performing controlled lab experiments. Next we test these sub-GHz modules in different real world environments such as open ground, straight road, moderately and densely wooded area, inside a concrete building and on building roof-tops. We then compare their performances for characterization of the wireless channels in different environments. In the end, we propose a sensor and network plan towards monitoring water resources inside the IISc campus.

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative α-entropies (denoted Iα), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative α-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative α-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Rényi or Tsallis entropy principle. The minimizing probability distribution (termed forward Iα-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse Iα-projection is studied.

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted ℐα) were studied. Such minimizers were called forward ℐα-projections. Here, a complementary class of minimization problems leading to the so-called reverse ℐα-projections are studied. Reverse ℐα-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (α > 1) and in constrained compression settings (αα-projection into a forward ℐα-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Representatives of several Internet service providers (ISPs) have expressed their wish to see a substantial change in the pricing policies of the Internet. In particular, they would like to see content providers (CPs) pay for use of the network, given the large amount of resources they use. This would be in clear violation of the “network neutrality” principle that had characterized the development of the wireline Internet. Our first goal in this article is to propose and study possible ways of implementing such payments and of regulating their amount. We introduce a model that includes the users' behavior, the utilities of the ISP and of the CPs, and, the monetary flow that involves the content users, the ISP and CP, and, in particular, the CP's revenues from advertisements. We consider various game models and study the resulting equilibria; they are all combinations of a noncooperative game (in which the ISPs and CPs determine how much they will charge the users) with a “cooperative” one on how the CP and the ISP share the payments. We include in our model a possible asymmetric weighting parameter (that varies between zero to one). We also study equilibria that arise when one of the CPs colludes with the ISP. We also study two dynamic game models as well as the convergence of prices to the equilibrium values.

We consider the problem of “fair” scheduling the resources to one of the many mobile stations by a centrally controlled base station (BS). The BS is the only entity taking decisions in this framework based on truthful information from the mobiles on their radio channel. We study the well-known family of parametric α-fair scheduling problems from a game-theoretic perspective in which some of the mobiles may be noncooperative. We first show that if the BS is unaware of the noncooperative behavior from the mobiles, the noncooperative mobiles become successful in snatching the resources from the other cooperative mobiles, resulting in unfair allocations. If the BS is aware of the noncooperative mobiles, a new game arises with BS as an additional player. It can then do better by neglecting the signals from the noncooperative mobiles. The BS, however, becomes successful in eliciting the truthful signals from the mobiles only when it uses additional information (signal statistics). This new policy along with the truthful signals from mobiles forms a Nash equilibrium (NE) that we call a Truth Revealing Equilibrium. Finally, we propose new iterative algorithms to implement fair scheduling policies that robustify the otherwise nonrobust (in presence of noncooperation) α-fair scheduling algorithms.

We consider all-cast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected links whose capacities are independent and identically distributed random variables. We study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely. We then provide a decentralized push-pull algorithm that asymptotically achieves this normalized sum rate without network coding.

We study the tradeoff between delivery delay and energy consumption in a delay-tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the message and the number of destinations that have received the message. We formulate the problem as a controlled continuous-time Markov chain and derive the optimal closed-loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ordinary differential equation (ODE) (i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open-loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed-loop policy.

We consider multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected edges whose capacities are independent and identically distributed random variables. We study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely. We then provide a decentralized push-pull algorithm that asymptotically achieves this normalized sum rate.

We consider a visual search problem studied by Sripati and Olson where the objective is to identify an oddball image embedded among multiple distractor images as quickly as possible. We model this visual search task as an active sequential hypothesis testing problem (ASHT problem). Chernoff in 1959 proposed a policy in which the expected delay to decision is asymptotically optimal. The asymptotics is under vanishing error probabilities. We first prove a stronger property on the moments of the delay until a decision, under the same asymptotics. Applying the result to the visual search problem, we then propose a “neuronal metric” on the measured neuronal responses that captures the discriminability between images. From empirical study we obtain a remarkable correlation (r = 0.90) between the proposed neuronal metric and speed of discrimination between the images. Although this correlation is lower than with the L1metric used by Sripati and Olson, this metric has the advantage of being firmly grounded in formal decision theory.

A central scheduling problem in wireless communications is that of allocating resources to one of many mobile stations that have a common radio channel. Much attention has been given to the design of efficient and fair scheduling schemes that are centrally controlled by a base station (BS) whose decisions depend on the channel conditions reported by each mobile. The BS is the only entity taking decisions in this framework. The decisions are based on the reports of mobiles on their radio channel conditions. In this paper, we study the scheduling problem from a game-theoretic perspective in which some of the mobiles may be noncooperative or strategic, and may not necessarily report their true channel conditions. We model this situation as a signaling game and study its equilibria. We demonstrate that the only Perfect Bayesian Equilibria (PBE) of the signaling game are of the babbling type: the noncooperative mobiles send signals independent of their channel states, the BS simply ignores them, and allocates channels based only on the prior information on the channel statistics. We then propose various approaches to enforce truthful signaling of the radio channel conditions: a pricing approach, an approach based on some knowledge of the mobiles' policies, and an approach that replaces this knowledge by a stochastic approximations approach that combines estimation and control. We further identify other equilibria that involve non-truthful signaling.

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

We study the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain and derive the optimal closed loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ODE (i.e., fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed loop policy.

We address the problem of allocating a single divisible good to a number of agents. The agents have concave valuation functions parameterized by a scalar type. The agents report only the type. The goal is to find allocatively efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria are of interest: the maximum ratio of budget surplus to efficient surplus, and the expected budget surplus, within the class of linear rebate functions. The goal is to minimize them. Assuming that the valuation functions are known, we show that both problems reduce to convex optimization problems, where the convex constraint sets are characterized by a continuum of half-plane constraints parameterized by the vector of reported types. We then propose a randomized relaxation of these problems by sampling constraints. The relaxed problem is a linear programming problem (LP). We then identify the number of samples needed for “near-feasibility” of the relaxed constraint set. Under some conditions on the valuation function, we show that value of the approximate LP is close to the optimal value. Simulation results show significant improvements of our proposed method over the Vickrey-Clarke-Groves (VCG) mechanism without rebates. In the special case of indivisible goods, the mechanisms in this paper fall back to those proposed by Moulin, by Guo and Conitzer, and by Gujar and Narahari, without any need for randomization. Extension of the proposed mechanisms to situations when the valuation functions are not known to the central planner are also discussed.

The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation property with a certain rate function, then the limiting guessing exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the rate function. Other sufficient conditions related to certain continuity properties of the information spectrum are briefly discussed. This approach highlights the importance of the information spectrum in determining the limiting guessing exponent. All known prior results are then re-derived as example applications of our unifying approach.

The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav and Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for i.i.d., Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other hand is established.

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Θ(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Θ(√n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Θ(1) time units per sample, the delay increases to Θ(√n log n). The number of transmissions in both cases is Θ(n) per histogram sample. The achieved Θ(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Θ(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

We consider the problem of centrally controlled 'fair' scheduling of resources to one of the many mobile stations connected to a base station (BS). The BS is the only entity making decisions in this framework based on truthful information from the mobiles on their radio channel. We study the well-known family of parametric α-fair scheduling problems from a game-theoretic perspective in which some of the mobiles may be noncooperative. We first show that if the BS is unaware of the noncooperative behavior from the mobiles, the noncooperative mobiles become successful in snatching the resources from the other cooperative mobiles, resulting in unfair allocations. If the BS is aware of the noncooperative mobiles, a new game arises with BS as an additional player. It can then do better by neglecting the signals from the noncooperative mobiles. The BS, however, becomes successful in eliciting the truthful signals from the mobiles only when it uses additional information (signal statistics). This new policy along with the truthful signals from mobiles forms a Nash Equilibrium (NE) called a Truth Revealing Equilibrium. Finally, we propose new iterative algorithms to implement fair scheduling policies that robustify the otherwise non-robust (in presence of noncooperation) α-fair scheduling algorithms.

We study in this paper the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers, taking into account the impact of these decisions on the behavior of intelligent mobile terminals who can connect to the base station that offers the best utility. We first study the SINR association-game: we determine the cells corresponding to each base stations, i.e. the locations at which mobile terminals prefer to connect to a given base station than to other. The signal to interference and noise ratio (SINR) is used as the quantity that determines the association. We make some surprising observations: (i) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; (ii) A cell corresponding to a BS may be the union of disconnected sub-cells. We then study the Stackelberg equilibrium in the combined BS location and mobile association problem: we determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider Stackelberg equilibria in two frequency systems with successive interference cancellation.

The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav & Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for iid, Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other hand is established.

Rate-constrained power minimization (PMIN) over a code division multiple-access (CDMA) channel with correlated noise is studied. PMIN is shown to be an instance of a separable convex optimization problem subject to linear ascending constraints. PMIN is further reduced to a dual problem of sumrate maximization (RMAX). The results highlight the underlying unity between PMIN, RMAX, and a problem closely related to PMIN but with linear receiver constraints. Subsequently, conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve PMIN. The algorithms yield an upper bound of 2N - 1 on the number of distinct sequences where N is the processing gain. The sequences generated using the proposed algorithms are in general real-valued. If a rate-splitting and multi-dimensional CDMA approach is allowed, the upper bound reduces to N distinct sequences, in which case the sequences can form an orthogonal set and be binary plusmn1-valued.

The downlink scheduling problem in multi-queue multi-server systems under channel uncertainty is considered. Two policies that make allocations based on predicted channel states are proposed. The first is an extension of the well-known dynamic backpressure policy to the uncertain channel case. The second is a variant that improves delay performance under light loads. The stability region of the system is characterised and the first policy is argued to be throughput optimal. A recently proposed policy of Kar et al has lesser complexity, but is shown to be throughput suboptimal. Further, simulations demonstrate better delay and backlog properties for both our policies at light loads.

Two decision versions of a combinatorial power minimization problem for scheduling in a time-slotted Gaussian multiple-access channel (GMAC) are studied in this paper. If the number of slots per second is a variable, the problem is shown to be NP-complete. If the number of time-slots per second is fixed, an algorithm that terminates in O (Length (I)N+1) steps is provided.

The problem of decentralized sequential detection with conditionally independent observations is studied. The sensors form a star topology with a central node called fusion center as the hub. The sensors make noisy observations of a parameter that changes from an initial state to a final state at a random time where the random change time has a geometric distribution. The sensors amplify and forward the observations over a wireless Gaussian multiple access channel and operate under either a power constraint or an energy constraint. The optimal transmission strategy at each stage is shown to be the one that maximizes a certain Ali-Silvey distance between the distributions for the hypotheses before and after the change. Simulations demonstrate that the proposed analog technique has lower detection delays when compared with existing schemes. Simulations further demonstrate that the energy-constrained formulation enables better use of the total available energy than the power-constrained formulation in the change detection problem.

Sequence design problems are considered in this paper. The problem of sum power minimization in a spread spectrum system can be reduced to the problem of sum capacity maximization, and vice versa. A solution to one of the problems yields a solution to the other. Subsequently, conceptually simple sequence design algorithms known to hold for the white-noise case are extended to the colored noise case. The algorithms yield an upper bound of 2N - L on the number of sequences where N is the processing gain and L the number of non-interfering subsets of users. If some users (at most N - 1) are allowed to signal along a limited number of multiple dimensions, then N orthogonal sequences suffice.

Close relationships between guessing functions and length functions are established. Good length functions lead to good guessing functions. In particular, guessing in the increasing order of Lempel-Ziv lengths has certain universality properties for finite-state sources. As an application, these results show that hiding the parameters of the key-stream generating source in a private key crypto-system may not enhance the privacy of the system, the privacy level being measured by the difficulty in brute-force guessing of the key stream.

We study the problem of decentralized sequential change detection with conditionally independent observations. The sensors form a star topology with a central node called fusion center as the hub. The sensors transmit a simple function of their observations in an analog fashion over a wireless Gaussian multiple access channel and operate under either a power constraint or an energy constraint. Simulations demonstrate that the proposed techniques have lower detection delays when compared with existing schemes. Moreover we demonstrate that the energy-constrained formulation enables better use of the total available energy than a power-constrained formulation.

This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. A notion of redundancy is first defined and a new divergence quantity that measures this redundancy is identified. This divergence quantity shares the Pythagorean property with the Kullback-Leibler divergence. Good guessing strategies that minimize the supremum redundancy (over the family) are then identified. The min-sup value measures the richness of the uncertainty set. The min-sup redundancies for two examples - the families of discrete memoryless sources and finite-state arbitrarily varying sources - are then determined

We study the problem of guessing the realization of a finite alphabet source, when some side information is provided, in a setting where the only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. We define a notion of redundancy, identify a quantity that measures this redundancy, and study its properties. We then identify good guessing strategies that minimize the supremum redundancy (over the family). The minimum value measures the richness of the uncertainty class

A conceptually simple proof for the capacity formula of an exponential server timing channel is provided. The proof links the timing channel to the point-process channel with instantaneous noiseless feedback. This point-process approach enables a study of timing channels that arise in multiserver queues, queues in tandem, and other simple configurations. Although the capacities of such channels remain to be found, the paper provides some analytical bounds and highlights a method to find achievable rates via simulations.

The sum capacity on a symbol-synchronous CDMA system having processing gain N and supporting K power constrained users can be achieved by employing at most 2N-1 sequences. Analogously, the minimum received power (energy-per-chip) on the symbol-synchronous CDMA system supporting K users that demand specified data rates can be attained by employing at most 2N-1 sequences. If there are L oversized users in the system, we need at most 2N-L-1 sequences. We show the above results by proving a converse to a well-known result of Weyl on the interlacing eigenvalues of the sum of two Hermitian matrices, one of which is of rank 1. The converse is analogous to a known converse to the interlacing eigenvalues theorem for bordering matrices.

To transmit information by timing arrivals to a single-server queue, we consider using the exponential server channel's maximum likelihood decoder. For any server with service times that are stationary and ergodic with mean 1//spl mu/ seconds, we show that the rate e/sup -1//spl mu/ nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate e/sup -1//spl mu//sub 1//spl mu//sub 2//(/spl mu//sub 1/+/spl mu//sub 2/) nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean 1//spl mu//sub 1/ seconds, and the arithmetic mean of the delays added by the server does not exceed 1//spl mu//sub 2/ seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues.

We show the existence of a good tree code with a sequential decoder for the exponential server timing channel. The expected number of computations before moving one step ahead is upper-bounded by a finite number. The rate of information transfer for this code is /spl mu//(2e) nats per second i.e., one half of the capacity. The cutoff rate for the exponential server queue is therefore at least /spl mu//(2u) nats per second.