Samar Agnihotri

Non-adaptive group testing: Explicit bounds and novel algorithms

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 sample-complexities of our algorithms are near-optimal with respect to known information-theoretic bounds.

Non-Adaptive Group Testing: Explicit Bounds and Novel Algorithms

We consider some computationally efficient and provably correct algorithms with near-optimal sample complexity for the problem of noisy nonadaptive 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 nonadaptive 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 flavors, 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 Fanos inequality and show that the upper and lower bounds are equal up to an explicitly computable universal constant factor (independent of problem parameters).

Amplify-and-forward in wireless relay networks

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 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 achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of such schemes in more complex relay networks which cannot be addressed in a straightforward manner with 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.

On maximizing lifetime of a sensor cluster

We consider the energy consumed in radio transmission by a set of sensors forming a data gathering wireless network. Our objective is to enhance the lifetime of such networks by exploiting three system-level opportunities. First, the number of bits to be transmitted can be reduced by taking advantage of the redundancy induced by spatio-temporal correlation in sensor data. Second, channel coding allows us to reduce transmission energy at the cost of increased transmission time. Third, sensor nodes can be expected to operate collaboratively, allowing optimal management of distributed energy resources. Our main contribution lies in providing a framework to merge these ideas for energy conscious networking. We pose the problem of maximizing network lifetime as an optimal scheduling problem. We consider a special case where the data rate is linearly proportional to received signal power, investigating both static and dynamic scheduling strategies. The optimal static schedule turns out to have a very simple form. For the dynamic case, we obtain an integer linear program formulation to find the optimal strategy. We then propose an efficient algorithm that exploits the special nature of the problem setting to find the optimal solution quickly. Finally, we consider the general case where data rates and signal power need not be linearly related and propose an algorithm to find the optimal transmission times subject to the deadline constraint imposed by the system.

Analog network coding in general SNR regime

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under two assumptions: (A) each relay node scales its received signal to the upper bound of its transmit power constraint, (B) the relay nodes in specific subsets of the network operate in the high-SNR regime. We establish that assumption (A), in general, leads to suboptimal end-to-end rate. We also characterize the performance of analog network coding in a class of symmetric layered networks without assumption (B). The key contribution of this work is a lemma that states that in a layered relay network a globally optimal set of scaling factors for the nodes that maximizes the end-to-end rate can be computed layer-by-layer. Specifically, a rate-optimal set of scaling factors for the nodes in a layer is the one that maximizes the sum-rate of the nodes in the next layer. This critical insight allows us to characterize analog network coding performance in network scenarios beyond those that can be analyzed using the existing approaches. We illustrate this by computing the maximum rate achievable with analog network coding in one particular layered network, in various communication scenarios.

Analog network coding in general SNR regime: Performance of a greedy scheme

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under certain assumptions on per node scaling factor and received SNR. Previously, we established a result that allows us to characterize the optimal performance of analog network coding in network scenarios beyond those that can be analyzed using the approaches based on such assumptions. The key contribution of this work is a scheme to greedily compute a lower bound to the optimal rate achievable with analog network coding in general layered networks. This scheme allows for exact computation of the optimal achievable rates in a wider class of layered networks than those that can be addressed using existing approaches. For the specific case of the Gaussian N-relay diamond network, to the best of our knowledge, the proposed scheme provides the first exact characterization of the optimal rate achievable with analog network coding. For general layered networks, our scheme allows us to compute optimal rates within a “small” gap from the cut-set upper bound asymptotically in the source power.

Enhancing Sensor Network Lifetime Using Interactive Communication

We are concerned with maximizing the lifetime of a data-gathering wireless sensor network consisting of set of nodes directly communicating with a base-station. We model this scenario as the m-message interactive communication between multiple correlated informants (sensor nodes) and a recipient (base-station). With this framework, we show that m-message interactive communication can indeed enhance network lifetime. Both worst-case and average-case performances are considered.

A new technique for improving quality of speech in voice over IP using time-scale modification

Packet arrival-delay variations and losses seriously affect the quality of voice delivered in VoIP. In this paper, using a time-scale modification algorithm, an integrated scheme is proposed to handle these impairments without introducing additional delays. This scheme provides flexible arrivaldelay cut-offs to late arriving packets, reducing the packet loss-rate at the receiver. Further, the lost packets are concealed effectively. Extensive simulations have shown that the proposed scheme delivers high-quality speech across widely varying packet arrival-delays and loss-rates. The proposed scheme is fully receiver-based and with its low computational complexity and generic nature, is applicable to any VoIP system.

A resource allocation scheme for device-to-device multicast in cellular networks

The potential of device-to-device (D2D) technology to support multicast services in LTE-Advanced networks has been recently realized. D2D communication brings great benefits to cellular networks in terms of enhanced spectral efficiency and larger coverage by enabling the devices to communicate directly with each other. D2D communication may lead to improved network capacity by sharing resources with cellular users (CUs). However, the resulting mutual interference may decrease or even outweigh the gain of D2D communication. In this paper, we propose a scheme to minimize the interference among D2D and CUs through a resource allocation scheme. We formulate the uplink resource allocation problem where a D2D multicast group can reuse resources of CUs under the constraint that the signal to interference plus noise ratio (SINR) requirements of CUs and D2D users are satisfied. We analyze a joint power and channel allocation scheme to maximize the total throughput of CUs and D2D users. The performance of D2D communication depends on maximum power constraint for the D2D users. Simulation results establish the efficacy of the proposed scheme.

Analog network coding in general SNR regime: Performance of network simplification

A communication scenario where a source communicates with a destination over a directed layered relay network is considered. Each relay performs analog network coding where it scales and forwards the signals received at its input. In this scenario, we address the question: What portion of the maximum end-to-end achievable rate can be maintained if only a fraction of relay nodes available at each layer are used? We consider, in particular, the Gaussian diamond network and a class of symmetric layered networks. For these networks we provide upper bounds on additive and multiplicative gaps between the optimal analog network coding performance when all N relays in each layer are used and when only k such relays are are used, k <; N (network simplification). We show that asymptotically (in source power), the additive gap increases at most logarithmically with ratio N/k and the number of layers, and the corresponding multiplicative gap increases at most linearly with ratio N/k and is independent of the number of layers in the layered network. To the best of our knowledge, this work offers the first characterization of the performance of network simplification in general layered amplify-and-forward relay networks. Further, unlike most of the current approximation results that attempt to bound optimal rates either within an additive gap or a multiplicative gap, our results suggest a new rate approximation scheme that allows for the simultaneous computation of additive and multiplicative gaps.