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Traditional reliability approaches introduce relevant costs to achieve unconditional correctness during data processing. However, many application environments are inherently tolerant to a certain degree of inexactness or inaccuracy. In this paper, we focus on the practical scenario of image processing in space, a domain where faults are a threat, while the applications are inherently tolerant to a certain degree of errors. We first introduce the concept of usability of the processed image to relax the traditional requirement of unconditional correctness, and to limit the computational overheads related to reliability. We then introduce our new flexible and lightweight fault management methodology for inaccurate application environments. A key novelty of our scheme is the utilization of neural networks to reduce the costs associated with the occurrence and the detection of faults. Experiments on two aerospace image processing case studies show overall time savings of 14.89% and 34.72% for the two applications, respectively, as compared with the baseline classical Duplication with Comparison scheme.

Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The considered scenario consists of several ground terminals (GTs) communicating with the UAVs using variable transmission power and fixed data rate. First, the static case of a fixed geographical GT density is analyzed. Using high resolution quantization theory, the corresponding best achievable performance (measured in terms of the average GT transmission power) is determined in the asymptotic regime of a large number of UAVs. Next, the dynamic case where the GT density is allowed to vary periodically through time is considered. For one-dimensional networks, an accurate formula for the total UAV movement that guarantees the best time-averaged performance is determined. In general, the tradeoff between the total UAV movement and the achievable performance is obtained through a Lagrangian approach. A corresponding trajectory optimization algorithm is introduced and shown to guarantee a convergent Lagrangian. Numerical simulations confirm the analytical findings. Extensions to different system models and performance measures are also discussed.

Abstract-Multi-tier networks have many applications in different fields. We define a novel two-tier quantizer that can be applied to different node deployment problems including the energy conservation in two-tier wireless sensor networks (WSNs) consisting of N access points (APs) and M fusion centers (FCs). We aim at finding an optimal deployment of APs and FCs to minimize the average weighted total, or Lagrangian, of sensor and AP powers. For one fusion center, M = 1, we show that the optimal deployment of APs is simply a linear transformation of the optimal N -level quantizer for density f , and the sole FC should be located at the geometric centroid of the sensing field. We also provide the exact expression of the AP-Sensor power function and prove its convexity. For more than one fusion center, M > 1, we provide a necessary condition for the optimal deployment. Furthermore, to numerically optimize the AP and FC deployment, we propose three Lloyd-like algorithms and analyze their convergence. Simulation results show that our algorithms outperform the existing algorithms.

We study quantized beamforming in wireless amplify-and-forward relay-interference networks with any number of transmitters, relays, and receivers. We design the quantizer of the channel state information to minimize the probability that at least one receiver incorrectly decodes its desired symbol(s). Correspondingly, we introduce a generalized diversity measure that encapsulates the conventional one as the first-order diversity. Additionally, it incorporates the second-order diversity, which is concerned with the transmitter power dependent logarithmic terms that appear in the error rate expression. First, we show that, regardless of the quantizer and the amount of feedback that is used, the relay-interference network suffers a second-order diversity loss compared to interference-free networks. Then, two different quantization schemes are studied: First, using a global quantizer, we show that a simple relay selection scheme can achieve maximal diversity. Then, using the localization method, we construct both fixedlength and variable-length local (distributed) quantizers (fLQs and vLQs). Our fLQs achieve maximal first-order diversity, whereas our vLQs achieve maximal diversity. Moreover, we show that all the promised diversity and array gains can be obtained with arbitrarily low feedback rates when the transmitter powers are sufficiently large. Finally, we confirm our analytical findings through simulations. Index TermsWireless relay network, beamforming, interference, distributed vector quantization, symbol error probability, diversity gain, array gain.

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We study a multiple-input single-output fading channel, where we would like to minimize the channel outage probability or symbol error rate (SER) by employing beamforming via quantized channel state information at the transmitter (CSIT). We consider a variable-length limited feedback scheme where the quantized CSIT is acquired through feedback binary codewords of possibly different lengths. We design and analyze the performance of the associated variable-length quantizers (VLQs) and compare their performance with the previously studied fixed-length quantizers (FLQs). For the outage probability performance measure, we construct VLQs that can achieve the full-CSIT performance with finite rate. Moreover, as the signal-to-noise ratio P tends to infinity, we show that VLQs can achieve the full-CSIT outage probability performance with asymptotically zero feedback rate. For the SER performance measure, we show that while the SER with full-CSIT is not achievable at any finite feedback rate, the diversity and array gains with full-CSIT can be achieved using VLQs with asymptotically zero feedback rate as P → ∞. Our results show that VLQs can significantly improve upon the traditional FLQs that require infinite feedback rate to achieve the outage probability or the diversity and array gains with full-CSIT.Index Terms-Multiple antenna systems, limited feedback, channel quantization, variable-length quantization, beamforming, outage probability, error probability, diversity and array gains.

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