Information Theory (cs.IT)

Abstract: We consider fairness scheduling in a user-centric cell-free massive MIMO network, where $L$ remote radio units, each with $M$ antennas, serve $K_{\rm tot} \approx LM$ user equipments (UEs). Recent results show that the maximum network sum throughput is achieved where $K_{\rm act} \approx \frac{LM}{2}$ UEs are simultaneously active in any given time-frequency slots. However, the number of users $K_{\rm tot}$ in the network is usually much larger. This requires that users are scheduled over the time-frequency resource and achieve a certain throughput rate as an average over the slots. We impose throughput fairness among UEs with a scheduling approach aiming to maximize a concave component-wise non-decreasing network utility function of the per-user throughput rates. In cell-free user-centric networks, the pilot and cluster assignment is usually done for a given set of active users. Combined with fairness scheduling, this requires pilot and cluster reassignment at each scheduling slot, involving an enormous overhead of control signaling exchange between network entities. We propose a fixed pilot and cluster assignment scheme (independent of the scheduling decisions), which outperforms the baseline method in terms of UE throughput, while requiring much less control information exchange between network entities.

Abstract: Convolutional codes with a maximum distance profile attain the largest possible column distances for the maximum number of time instants and thus have outstanding error-correcting capability especially for streaming applications. Explicit constructions of such codes are scarce in the literature. In particular, known constructions of convolutional codes with rate k/n and a maximum distance profile require a field of size at least exponential in n for general code parameters. At the same time, the only known lower bound on the field size is the trivial bound that is linear in n. In this paper, we show that a finite field of size $\Omega_L(n^{L-1})$ is necessary for constructing convolutional codes with rate k/n and a maximum distance profile of length L. As a direct consequence, this rules out the possibility of constructing convolutional codes with a maximum distance profile of length L >= 3 over a finite field of size O(n). Additionally, we also present an explicit construction of convolutional code with rate k/n and a maximum profile of length L = 1 over a finite field of size $O(n^{\min\{k,n-k\}})$, achieving a smaller field size than known constructions with the same profile length.

Abstract: With countless promising applications in various domains such as IoT and industry 4.0, task-oriented communication design (TOCD) is getting accelerated attention from the research community. This paper presents a novel approach for designing scalable task-oriented quantization and communications in cooperative multi-agent systems (MAS). The proposed approach utilizes the TOCD framework and the value of information (VoI) concept to enable efficient communication of quantized observations among agents while maximizing the average return performance of the MAS, a parameter that quantifies the MAS's task effectiveness. The computational complexity of learning the VoI, however, grows exponentially with the number of agents. Thus, we propose a three-step framework: i) learning the VoI (using reinforcement learning (RL)) for a two-agent system, ii) designing the quantization policy for an $N$-agent MAS using the learned VoI for a range of bit-budgets and, (iii) learning the agents' control policies using RL while following the designed quantization policies in the earlier step. We observe that one can reduce the computational cost of obtaining the value of information by exploiting insights gained from studying a similar two-agent system - instead of the original $N$-agent system. We then quantize agents' observations such that their more valuable observations are communicated more precisely. Our analytical results show the applicability of the proposed framework under a wide range of problems. Numerical results show striking improvements in reducing the computational complexity of obtaining VoI needed for the TOCD in a MAS problem without compromising the average return performance of the MAS.

Abstract: The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality condition and utilizing preshared entanglement between the sender and receiver. In this paper, a new family of EAQECCs is constructed from negacyclic codes of length $n=\frac{q^2+1}{a}$, where $q$ is an odd prime power, $a=\frac{m^2+1}{2}$ and $m$ is an odd integer. Some new entanglement-assisted quantum maximum distance separable (EAQMDS) codes are obtained in the sense that their parameters are not covered by the previously known ones.

Abstract: We introduce a new operational technique for deriving chain rules for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator algebra or norm interpolation. Instead, our framework considers a simple information transmission task and obtains lower and upper bounds for it. The lower bounds are obtained by leveraging a successive cancellation encoding and decoding technique. Pitting the upper and lower bounds against each other gives us the desired chain rule. As a demonstration of this technique, we derive chain rules for the smooth max mutual information and the smooth-Hypothesis testing mutual information.

Abstract: Intelligent reflecting surface (IRS) is a promising and disruptive technique to extend the network coverage and improve spectral efficiency. This paper investigates an IRS-assisted Terahertz (THz) multiple-input multiple-output (MIMO)-nonorthogonal multiple access (NOMA) system based on hybrid precoding in the presence of eavesdropper. Two types of sparse RF chain antenna structures are adopted, i.e., sub-connected structure and fully connected structure. Cluster heads are firstly selected for transmissions, and discrete phase-based analog precoding is designed for the transmit beamforming. Subsequently, based on the channel conditions, the users are grouped into multiple clusters, and each cluster is transmitted by using the NOMA technique. In addition, a low complexity zero-forcing method is employed to design digital precoding so as to eliminate interference between clusters. On this basis, we propose a secure transmission scheme to maximize the sum secrecy rate by jointly optimizing the power allocation and phase shifts of IRS under the constraints of system transmission power, achievable rate requirement of each user, and IRS phase shifts. Due to multiple coupled variables, the formulated problem leads to a non-convex issue. We apply the Taylor series expansion and semidefinite programming to convert the original non-convex problem into a convex one. Then, an alternating optimization algorithm is developed to obtain a feasible solution of the original problem. Simulation results are demonstrated to validate the convergence of the proposed algorithm, and confirm that the deployment of IRS can significantly improve the secrecy performance.

Abstract: Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in social systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression discontinuity from econometrics assumes the existence of a discontinuous variable that splits the population into distinct partitions to estimate the causal effects of a given phenomenon. Here we consider the design of partitions for a given discontinuous variable to optimize a certain effect previously studied using regression discontinuity. To do so, we propose a quantization-theoretic approach to optimize the effect of interest, first learning the causal effect size of a given discontinuous variable and then applying dynamic programming for optimal quantization design of discontinuities that balance the gain and loss in the effect size. We also develop a computationally-efficient reinforcement learning algorithm for the dynamic programming formulation of optimal quantization. We demonstrate our approach by designing optimal time zone borders for counterfactuals of social capital, social mobility, and health. This is based on regression discontinuity analyses we perform on novel data, which may be of independent empirical interest in showing a causal relationship between sunset time and social capital.

Abstract: Few-weight codes over finite chain rings are associated with combinatorial objects such as strongly regular graphs (SRGs), strongly walk-regular graphs (SWRGs) and finite geometries, and are also widely used in data storage systems and secret sharing schemes. The first objective of this paper is to characterize all possible parameters of Plotkin-optimal two-homogeneous weight regular projective codes over finite chain rings, as well as their weight distributions. We show the existence of codes with these parameters by constructing an infinite family of two-homogeneous weight codes. The parameters of their Gray images have the same weight distribution as that of the two-weight codes of type SU1 in the sense of Calderbank and Kantor (Bull Lond Math Soc 18: 97-122, 1986). Further, we also construct three-homogeneous weight regular projective codes over finite chain rings combined with some known results. Finally, we study applications of our constructed codes in secret sharing schemes and graph theory. In particular, infinite families of SRGs and SWRGs with non-trivial parameters are obtained.

Abstract: The research on the sixth-generation (6G) wireless communications for the development of future mobile communication networks has been officially launched around the world. 6G networks face multifarious challenges, such as resource-constrained mobile devices, difficult wireless resource management, high complexity of heterogeneous network architectures, explosive computing and storage requirements, privacy and security threats. To address these challenges, deploying blockchain and artificial intelligence (AI) in 6G networks may realize new breakthroughs in advancing network performances in terms of security, privacy, efficiency, cost, and more. In this paper, we provide a detailed survey of existing works on the application of blockchain and AI to 6G wireless communications. More specifically, we start with a brief overview of blockchain and AI. Then, we mainly review the recent advances in the fusion of blockchain and AI, and highlight the inevitable trend of deploying both blockchain and AI in wireless communications. Furthermore, we extensively explore integrating blockchain and AI for wireless communication systems, involving secure services and Internet of Things (IoT) smart applications. Particularly, some of the most talked-about key services based on blockchain and AI are introduced, such as spectrum management, computation allocation, content caching, and security and privacy. Moreover, we also focus on some important IoT smart applications supported by blockchain and AI, covering smart healthcare, smart transportation, smart grid, and unmanned aerial vehicles (UAVs). We also analyze the open issues and research challenges for the joint deployment of blockchain and AI in 6G wireless communications. Lastly, based on lots of existing meaningful works, this paper aims to provide a comprehensive survey of blockchain and AI in 6G networks.

Abstract: Approximate message passing (AMP) is a scalable, iterative approach to signal recovery. For structured random measurement ensembles, including independent and identically distributed (i.i.d.) Gaussian and rotationally-invariant matrices, the performance of AMP can be characterized by a scalar recursion called state evolution (SE). The pseudo-Lipschitz (polynomial) smoothness is conventionally assumed. In this work, we extend the SE for AMP to a new class of measurement matrices with independent (not necessarily identically distributed) entries. We also extend it to a general class of functions, called controlled functions which are not constrained by the polynomial smoothness; unlike the pseudo-Lipschitz function that has polynomial smoothness, the controlled function grows exponentially. The lack of structure in the assumed measurement ensembles is addressed by leveraging Lindeberg-Feller. The lack of smoothness of the assumed controlled function is addressed by a proposed conditioning technique leveraging the empirical statistics of the AMP instances. The resultants grant the use of the SE to a broader class of measurement ensembles and a new class of functions.

Abstract: In this article, we construct linear codes over the commutative non-unital ring $I$ of size four. We obtain their Lee-weight distributions and study their binary Gray images. Under certain mild conditions, these classes of binary codes are minimal and self-orthogonal. All codes in this article are few-weight codes. Besides, an infinite class of these binary codes consists of distance optimal codes with respect to the Griesmer bound.