1 . We present computationally efficient and provably correct algorithms with near-optimal sample-complexity for noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each pool is then tested to identify the defective items, which are usually assumed to be sparsely distributed. We consider random non-adaptive pooling where pools are selected randomly and independently of the test outcomes. Our noisy scenario accounts for both false negatives and false positives for the test outcomes. Inspired by compressive sensing algorithms we introduce four novel computationally efficient decoding algorithms for group testing, CBP via Linear Programming (CBP-LP), NCBP-LP (Noisy CBP-LP), and the two related algorithms NCBP-SLP+ and NCBP-SLP-("Simple" NCBP-LP). The first of these algorithms deals with the noiseless measurement scenario, and the next three with the noisy measurement scenario. We derive explicit sample-complexity bounds-with all constants made explicit-for these algorithms as a function of the desired error probability; the noise parameters; the number of items; and the size of the defective set (or an upper bound on it). We show that the samplecomplexities of our algorithms are near-optimal with respect to known information-theoretic bounds.
Abstract-We consider some computationally efficient and provably correct algorithms with near-optimal sample-complexity for the problem of noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each pool is then tested to identify the defective items, which are usually assumed to be "sparse". We consider non-adaptive randomly pooling measurements, where pools are selected randomly and independently of the test outcomes. We also consider a model where noisy measurements allow for both some false negative and some false positive test outcomes (and also allow for asymmetric noise, and activation noise). We consider three classes of algorithms for the group testing problem (we call them specifically the "Coupon Collector Algorithm", the "Column Matching Algorithms", and the "LP Decoding Algorithms" -the last two classes of algorithms (versions of some of which had been considered before in the literature) were inspired by corresponding algorithms in the Compressive Sensing literature. The second and third of these algorithms have several flavours, dealing separately with the noiseless and noisy measurement scenarios. Our contribution is novel analysis to derive explicit sample-complexity bounds -with all constants expressly computed -for these algorithms as a function of the desired error probability; the noise parameters; the number of items; and the size of the defective set (or an upper bound on it). We also compare the bounds to information-theoretic lower bounds for sample complexity based on Fano's inequality and show that the upper and lower bounds are equal up to an explicitly computable universal constant factor (independent of problem parameters).
A general class of wireless relay networks with a single source-destination pair is considered.Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals.In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplifyand-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches.Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.
This paper proposes a mathematical fractional order modelling of Voltage Source Converters (VSC). Fractional behaviour helps to model and describe a real object more accurately than the integer order model. State-space equations of VSC is obtained using fractional calculus in d-q domain. The Caputo derivative method is employed to eliminate complex definitions of fractional calculus and to get approximate solution with optimal design of parameters. A detailed analysis is performed on developed mathematical fractional order model of VSC including small-signal analysis and DC analysis. The stability and time-domain transient analysis is carried out to validate the fractional order VSC for its application as Distribution STATtic COMpensator (DSTATCOM) in power distribution system, using real-time simulator. Fractional-order capacitor and inductor are designed and modelled for verification of fractional order VSC through simulations. The real-time simulation results verify the effectiveness of proposed model. It shows that fractional order model can describe the operating characteristics of VSC more accurately. The comparative performance analysis demonstrates superior transient response in case of fractional order devices as compared to integer order.
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