Computer Science

In the problem of classical group testing one aims to identify a small subset (of expected size d ) diseased individuals/defective items in a large population (of size n ) based on a minimal number of suitably-designed group non-adaptive tests on subsets of items, where the test outcome is governed by an "OR" function, i.e., the test outcome is positive iff the given test contains at least one defective item. Motivated by physical considerations we consider a generalized scenario (that includes as special cases multiple other group-testing-like models in the literature) wherein the test outcome is governed by an arbitrary monotone (stochastic) test function f(?? , with the test outcome being positive with probability f(x) , where x is the number of defectives tested in that pool. For any monotone test function f(?? we present a non-adaptive generalized group-testing scheme that identifies all defective items with high probability. Our scheme requires at most O( d 2 log(n)) tests for any monotone test function f(?? , and at most O(dlog(n)) in the physically relevant sub-class of sensitive test functions (and hence is information-theoretically order-optimal for this sub-class).

We consider globally optimal precoder design for rate splitting multiple access in Gaussian multiple-input single-output downlink channels with respect to weighted sum rate and energy efficiency maximization. The proposed algorithm solves an instance of the joint multicast and unicast beamforming problem and includes multicast- and unicast-only beamforming as special cases. Numerical results show that it outperforms state-of-the-art algorithms in terms of numerical stability and converges almost twice as fast.

In this paper, we study the \emph{type graph}, namely a bipartite graph induced by a joint type. We investigate the maximum edge density of induced bipartite subgraphs of this graph having a number of vertices on each side on an exponential scale. This can be seen as an isoperimetric problem. We provide asymptotically sharp bounds for the exponent of the maximum edge density as the blocklength goes to infinity. We also study the biclique rate region of the type graph, which is defined as the set of ( R 1 , R 2 ) such that there exists a biclique of the type graph which has respectively e n R 1 and e n R 2 vertices on two sides. We provide asymptotically sharp bounds for the biclique rate region as well. We then apply our results and proof ideas to noninteractive simulation problems. We completely characterize the exponents of maximum and minimum joint probabilities when the marginal probabilities vanish exponentially fast with given exponents. These results can be seen as strong small-set expansion theorems. We extend the noninteractive simulation problem by replacing Boolean functions with arbitrary nonnegative functions, and obtain new hypercontractivity inequalities which are stronger than the common hypercontractivity inequalities. Furthermore, as an application of our results, a new outer bound for the zero-error capacity region of the binary adder channel is provided, which improves the previously best known bound, due to Austrin, Kaski, Koivisto, and Nederlof. Our proofs in this paper are based on the method of types, linear algebra, and coupling techniques.

This paper considers grid formation of an unmanned aerial vehicle (UAV) swarm for maximizing the secrecy rate in the presence of an unknown eavesdropper. In particular, the UAV swarm performs coordinated beamforming onto the null space of the legitimate channel to jam the eavesdropper located at an unknown location. By nulling the channel between the legitimate receiver and the UAV swarm, we obtain an optimal trajectory and jamming power allocation for each UAV enabling wideband single ray beamforming to improve the secrecy rate. Results obtained demonstrate the effectiveness of the proposed UAV-aided jamming scheme as well as the optimal number of UAVs in the swarm necessary to observe a saturation effect in the secrecy rate. We also show the optimal radius of the unknown but constrained location of the eavesdropper.

In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring M k (R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring M k (R) are one sided ideals in the group matrix ring M k (R)G and the corresponding codes over the ring R are G k -codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72,36,12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type~I and 4 new Type~II binary [72,36,12] self-dual codes.

Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the study of practical noise models, a prominent one being dilution noise. Under the dilution noise model, items in a test pool have an i.i.d. probability of being diluted, meaning their contribution to a test does not take effect. In this setting, we investigate the number of tests required to achieve vanishing error probability with respect to existing algorithms and provide an algorithm-independent converse bound. In contrast to other noise models, we also encounter the interesting phenomenon that dilution noise on the resulting test outcomes can be offset by choosing a suitable noise-level-dependent Bernoulli test design, resulting in matching achievability and converse bounds up to order in the high noise regime.

We propose a novel infection spread model based on a random connection graph which represents connections between n individuals. Infection spreads via connections between individuals and this results in a probabilistic cluster formation structure as well as a non-i.i.d. (correlated) infection status for individuals. We propose a class of two-step sampled group testing algorithms where we exploit the known probabilistic infection spread model. We investigate the metrics associated with two-step sampled group testing algorithms. To demonstrate our results, for analytically tractable exponentially split cluster formation trees, we calculate the required number of tests and the expected number of false classifications in terms of the system parameters, and identify the trade-off between them. For such exponentially split cluster formation trees, for zero-error construction, we prove that the required number of tests is O( log 2 n) . Thus, for such cluster formation trees, our algorithm outperforms any zero-error non-adaptive group test, binary splitting algorithm, and Hwang's generalized binary splitting algorithm. Our results imply that, by exploiting probabilistic information on the connections of individuals, group testing can be used to reduce the number of required tests significantly even when infection rate is high, contrasting the prevalent belief that group testing is useful only when infection rate is low.

In reconfigurable intelligent surfaces (RISs) aided communications, the existing passive beamforming (PB) design involves polynomial complexity in the number of reflecting elements, and thus is difficult to implement due to a massive number of reflecting elements. To overcome this difficulty, we propose a reflection-angle-based cascaded channel model by adopting the generalized Snell's law, in which the dimension of the variable space involved in optimization is significantly reduced, resulting in a simplified hierarchical passive beamforming (HPB) design. We develop an efficient two-stage HPB algorithm, which exploits the angular domain property of the channel, to maximize the achievable rate of the target user. Simulation results demonstrate the appealing performance and low complexity of the proposed HPB design.

A main challenge of 5G and beyond wireless systems is to efficiently utilize the available spectrum and simultaneously reduce the energy consumption. From the radio resource allocation perspective, the solution to this problem is to maximize the energy efficiency instead of the throughput. This results in the optimal benefit-cost ratio between data rate and energy consumption. It also often leads to a considerable reduction in throughput and, hence, an underutilization of the available spectrum. Contemporary approaches to balance these metrics based on multi-objective programming theory often lack operational meaning and finding the correct operating point requires careful experimentation and calibration. Instead, we propose the novel concept of hierarchical resource allocation where conflicting objectives are ordered by their importance. This results in a resource allocation algorithm that strives to minimize the transmit power while keeping the data rate close the maximum achievable throughput. In a typical multi-cell scenario, this strategy is shown to reduces the transmit power consumption by 65% at the cost of a 5% decrease in throughput. Moreover, this strategy also saves energy in scenarios where global energy efficiency maximization fails to achieve any gain over throughput maximization.

In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by receiving quantum information from the servers. The QPIR problem has been treated by Song et al. in the case of replicated servers, both with and without collusion. QPIR over [n,k] maximum distance separable (MDS) coded servers was recently considered by Allaix et al., but the collusion was essentially restricted to t=n?�k servers in the sense that a smaller t would not improve the retrieval rate. In this paper, the QPIR setting is extended to allow for retrieval with high rate for any number of colluding servers t with 1?�t?�n?�k . Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts, as well as those of the previously proposed coded and colluding QPIR schemes. This is enabled by considering the stabilizer formalism and weakly self-dual generalized Reed--Solomon (GRS) star product codes.