Abstracts:The conventional Cohen’s distribution can’t meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we embark on blending time-frequency operators and coordinate operator fractionizations to formulate the definition of the joint fractionizations metaplectic Wigner distribution (JFMWD), based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen’s distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the JFMWD domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including the classical Gaussian filter, the Cohen’s distribution filtering methods with fixed kernel functions, the classical Wiener filter, the adaptive generalized linear canonical convolution-based filtering method, the adaptive Cohen’s distribution filtering method, the adaptive JFMWD-based Cohen’s distribution filtering method, and the adaptive generalized metaplectic convolution-based Cohen’s distribution filtering method in noise suppression.

Abstracts:Quasi complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. In this paper, we first derive a tighter bound on the maximum aperiodic correlation among all constituent complementary sequence sets in QCSSs. By proposing a new combinatorial structure called quasi-Florentine rectangles, we obtain a new construction of QCSSs with large set sizes. Using Butson-type Hadamard matrices and quasi-Florentine rectangles, we propose another construction which can construct QCSSs with flexible parameters over any given alphabet size, including small alphabets. All the proposed sequences are optimal with respect to the newly proposed bound. Also, through some of the constructions, the column sequence PMEPR of the proposed QCSSs are upper bounded by 2.

Abstracts:A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to w, a CAC of length L with weight w can provide a hard guarantee that each active user has at least one successful transmission within every consecutive L slots. In this paper, we generalize some previously known constructions of constant-weight CACs, and then derive several classes of optimal CACs by the help of Kneser’s Theorem and some techniques in Additive Combinatorics. Another spotlight of this paper is to relax the identical-weight constraint in prior studies to study mixed-weight CACs for the first time, for the purpose of increasing the throughput and reducing the access delay of some potential users with higher priority. As applications of those obtained optimal CACs, we derive some classes of optimal mixed-weight CACs.

Abstracts:A power assignment over parallel Gaussian broadcast channels splits a power budget at the access point among all channel-user pairs subject to per-channel upper-bounds on the sum-power, and yields a rate allocation to all channel-user pairs. Its weighted energy efficiency (WEE) is the ratio of its weighted sum-rate over its sum-power plus a fixed positive overhead. The problem Max-WEE seeks a power assignment maximizing the WEE. Special variants of Max-WEE with unit weights or two users per channel have been extensively studied in the literature. But none of the existing algorithms for those special variants have known bounds on running time, mainly because they follow the general-purposed methods for fractional programming. In this paper, we first derive fundamental properties and closed-form expressions of maximum WEE. Then we devise a simple water-filling algorithm for Max-WEE. Assuming all users are presorted by weight, the water-filling algorithm has linear complexity in the number of channel-user pairs. Under a mild presorting condition, we further develop a linear-complexity algorithm for Max-WEE subject to rate demand.

Abstracts:This paper studies an internet of things (IoT) network where a fusion center relies on multi-view and correlated information generated by multiple sources to monitor various regions. Each region possesses hard age of correlated information (AoCI) constraints for information update, and accordingly we propose a scheduling policy to satisfy such needs and minimize the required wireless resources. We first approximate the problem to a dual bin-packing problem. Secondly, efficient scheduling policies are identified when the age constraints possess special mathematical properties, where the number of channels at most required is analyzed. Optimality conditions of the proposed policies are presented. For general constraints, a two-step grouping algorithm for multi-view (TGAM) is proposed to establish scheduling policies. Under TGAM, the constraints are mapped into a combination of the special constraints. To quickly identify an optimized mapping from a vast solution space, TGAM heuristically groups the regions according to their constraints and then searches for the optimal mapping for each group. Numerical results demonstrate that, compared to a derived lower bound, the proposed TGAM requires only 1.07% more channels. Additionally, the number of regions that can be served by TGAM is significantly larger than the state-of-the art algorithm, given the number of channels.

Abstracts:This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a computationally efficient coding method which overcomes the drawbacks of the Fractional Repetition Coding gradient coding method proposed by Tandon et al., and can also be leveraged by coded computing networks whose servers are of heterogeneous nature. Specifically, we propose a construction for fractional repetition gradient coding; while ensuring that the generator matrix remains close to perfectly balanced for any set of coding parameters, as well as a low complexity decoding step. The proposed binary encoding avoids operations over the real and complex numbers which inherently introduce numerical and rounding errors, thereby enabling accurate distributed encodings of the partial gradients. We then make connections between gradient coding and coded matrix multiplication. Specifically, we show that any gradient coding scheme can be extended to coded matrix multiplication. Furthermore, we show how the proposed binary gradient coding scheme can be used to construct two different coded matrix multiplication schemes, each achieving different trade-offs.

Abstracts:Coded distributed computing can reduce the communication load for distributed computing systems by introducing redundant computation and creating multicasting opportunities. However, the existing schemes require delicate data placement and output function assignment, which is not feasible when distributed nodes fetch data without the orchestration of a central server. In this paper, we consider the general systems where the data placement and output function assignment are arbitrary but pre-set. We propose two coded computing schemes, One-shot Coded Transmission (OSCT) and Few-shot Coded Transmission (FSCT), to reduce the communication load. Both schemes first group the nodes into clusters and divide the transmission of each cluster into multiple rounds, and then design coded transmission in each round to maximize the multicast gain. The key difference between OSCT and FSCT is that the former uses a one-shot transmission where each encoded message can be decoded independently by the intended nodes, while the latter allows each node to jointly decode multiple received symbols to achieve potentially larger multicast gains. Furthermore, based on the lower bound proposed by Yu et al., we derive sufficient conditions for the optimality of OSCT and FSCT, respectively. This not only recovers the existing optimality results but also includes some cases where our schemes are optimal while others are not.

Abstracts:We study the fundamental limits of covert communications over general memoryless additive-noise channels. We assume that the legitimate receiver and the eavesdropper share the same channel and therefore see the same outputs. Under mild integrability assumptions, we find a general upper bound on the square-root scaling constant, which only involves the variance of the logarithm of the probability density function of the noise. Furthermore, we show that, under some additional assumptions, this upper bound is tight. We also provide upper bounds on the length of the secret key required to achieve the optimal scaling.

Abstracts:Noiseless private side information does not reduce the download cost in Symmetric Private Information Retrieval (SPIR) unless the client knows all but one file. While this is a pessimistic result, we explore in this paper whether noisy client side information available at the client helps decrease the download cost in the context of SPIR with colluding and replicated servers. Specifically, we assume that the client possesses noisy side information about each stored file, which is obtained by passing each file through one of D possible discrete memoryless test channels. The statistics of the test channels are known by the client and by all the servers, but the mapping $\boldsymbol {\mathcal {M}}$ between the files and the test channels is unknown to the servers. We study this problem under two privacy metrics. Under the first metric, the client wants to preserve the privacy of its file selection and the mapping $\boldsymbol {\mathcal {M}}$ , and the servers want to preserve the privacy of all the non-selected files. Under the second metric, the client is willing to reveal the index of the test channel that is associated with its desired file. For both privacy metrics, we derive the optimal common randomness and download cost. Our setup generalizes SPIR with colluding servers and SPIR with private noiseless side information. Unlike noiseless side information, our results demonstrate that noisy side information can reduce the download cost, even when the client does not have noiseless knowledge of all but one file.

Abstracts:We develop a general framework for clustering and distribution matching problems with bandit feedback. We consider a K-armed bandit model where some subset of K arms is partitioned into M groups. Within each group, the random variable associated to each arm follows the same distribution on a finite alphabet. At each time step, the decision maker pulls an arm and observes its outcome from the random variable associated to that arm. Subsequent arm pulls depend on the history of arm pulls and their outcomes. The decision maker has no knowledge of the distributions of the arms or the underlying partitions. The task is to devise an online algorithm to learn the underlying partition of arms with the least number of arm pulls on average and with an error probability not exceeding a pre-determined value $\delta $ . Several existing problems fall under our general framework, including finding M pairs of arms, odd arm identification, and N-ary clustering of K arms belong to our general framework. We derive a non-asymptotic lower bound on the average number of arm pulls for any online algorithm with an error probability not exceeding $\delta $ . Furthermore, we develop a computationally-efficient online algorithm based on the Track-and-Stop method and Frank-Wolfe algorithm, and show that the average number of arm pulls of our algorithm asymptotically matches that of the lower bound. Our refined analysis also uncovers a novel bound on the speed at which the average number of arm pulls of our algorithm converges to the fundamental limit as $\delta $ vanishes.