Explicit and Optimal Codes for Distributed Storage

In the distributed storage coding problem we consider, data is stored across n nodes in a network, each capable of storing � symbols. It is required that the complete data can be reconstructed by downloading data from any k nodes. There is also the key additional requirement that a failed node be regenerated by connecting to any d nodes and downloading �symbols from each of them. Our goal is to minimize the repair bandwidth d�. In this paper we provide explicit constructions for several parameter sets of interest.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Optimal Power and Noise for Analog and Digital Sections of a Low Power Radio Receiver

We determine the optimal allocation of power between the analog and digital sections of an RF receiver while meeting the BER constraint. Unlike conventional RF receiver designs, we treat the SNR at the output of the analog front end (SNRAD) as a design parameter rather than a specification to arrive at this optimal allocation. We first determine the relationship of the SNRAD to the resolution and operating frequency of the digital section. We then use power models for the analog and digital sections to solve the power minimization problem. As an example, we consider a 802.15.4 compliant low-IF receiver operating at 2.4 GHz in 0.13 μm technology with 1.2 V power supply. We find that the overall receiver power is minimized by having the analog front end provide an SNR of 1.3dB and the ADC and the digital section operate at 1-bit resolution with 18MHz sampling frequency while achieving a power dissipation of 7mW.

Optimal Sleep-Wake Scheduling for Quickest Intrusion Detection using wireless sensor Networks

We consider the problem of quickest detection of an intrusion using a sensor network, keeping only a minimal number of sensors active. By using a minimal number of sensor devices,we ensure that the energy expenditure for sensing, computation and communication is minimized (and the lifetime of the network is maximized). We model the intrusion detection (or change detection) problem as a Markov decision process (MDP). Based on the theory of MDP, we develop the following closed loop sleep/wake scheduling algorithms: 1) optimal control of Mk+1, the number of sensors in the wake state in time slot k + 1, 2) optimal control of qk+1, the probability of a sensor in the wake state in time slot k + 1, and an open loop sleep/wake scheduling algorithm which 3) computes q, the optimal probability of a sensor in the wake state (which does not vary with time),based on the sensor observations obtained until time slot k.Our results show that an optimum closed loop control onMk+1 significantly decreases the cost compared to keeping any number of sensors active all the time. Also, among the three algorithms described, we observe that the total cost is minimum for the optimum control on Mk+1 and is maximum for the optimum open loop control on q.

Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

Impact of Energy Expenditure Rate Constraints on the performance of Multihop Wireless Mesh Networks

In this article we study the problem of joint congestion control, routing and MAC layer scheduling in multi-hop wireless mesh network, where the nodes in the network are subjected to maximum energy expenditure rates. We model link contention in the wireless network using the contention graph and we model energy expenditure rate constraint of nodes using the energy expenditure rate matrix. We formulate the problem as an aggregate utility maximization problem and apply duality theory in order to decompose the problem into two sub-problems namely, network layer routing and congestion control problem and MAC layer scheduling problem. The source adjusts its rate based on the cost of the least cost path to the destination where the cost of the path includes not only the prices of the links in it but also the prices associated with the nodes on the path. The MAC layer scheduling of the links is carried out based on the prices of the links. We study the e�ects of energy expenditure rate constraints of the nodes on the optimal throughput of the network.

Exploring use of climate information for optimal design of water resources infrastructure

We conducted surveys of fire and fuels managers at local, regional, and national levels to gain insights into decision processes and information flows in wildfire management. Survey results in the form of fire managers’ decision calendars show how climate information needs vary seasonally, over space, and through the organizational network, and help determine optimal points for introducing climate information and forecasts into decision processes. We identified opportunities to use climate information in fire management, including seasonal to interannual climate forecasts at all organizational levels, to improve the targeting of fuels treatments and prescribed burns, the positioning and movement of initial attack resources, and staffing and budgeting decisions. Longer-term (5–10 years) outlooks also could be useful at the national level in setting budget and research priorities. We discuss these opportunities and examine the kinds of organizational changes that could facilitate effective use of existing climate information and climate forecast capabilities.