This paper studies the information theoretic secure aggregation problem in a three-layer hierarchical network with arbitrary heterogeneous data assignment, where clustered users communicate with an aggregation server through an intermediate layer of relays. We consider a more general setting with arbitrary heterogeneous data assignment across users, where `arbitrary' means that the data assignment is given in advance and `heterogeneous' means that the users may hold different numbers of datasets. Each user locally computes the partially aggregated gradients as its input based on the assigned datasets and transmits masked input to its associated relay. The relays then forward the aggregated messages to the server, which aims to recover the sum of the gradients. In this process, while some users may drop out unpredictably, the server needs to correctly recover the desired aggregation from the surviving users. Moreover, the server or any relay may collude with a subset of users. We impose the following security constraints: (i) server security, requiring the server to learn only the sum of gradients without gaining any additional information about individual inputs; and (ii) relay security, ensuring that each relay learns nothing about users' inputs. Under these constraints, we propose an aggregation scheme that guarantees information theoretic security and achieves the optimal two-layer communication loads.

This paper considers a new secure gradient coding problem with uncoded groupwise keys, formalized as a (K, N, N_r, M, S) secure gradient coding model, where a user aims to compute the sum of the gradients from K datasets with the assistance of N distributed servers. We consider arbitrary heterogeneous data assignment, where each dataset is assigned to at least M servers. The user should recover the sum of gradients from the transmissions of any N_r servers. The security constraint guarantees that even if the user receives the transmitted messages from all servers, it cannot obtain any other information about the datasets except the sum of gradients. Compared to existing secure gradient coding works, we introduce a practical constraint on secret keys, namely uncoded groupwise keys, where the keys are mutually independent and each key is shared by precisely S servers. An achievable secure gradient coding scheme with uncoded groupwise keys is proposed, which is then proven to be optimal if S > M and to be order optimal within a factor of 2 otherwise.

Large-scale decentralized learning frameworks such as federated learning (FL), require both communication efficiency and strong data security, motivating the study of secure aggregation (SA). While information-theoretic SA is well understood in centralized and fully connected networks, its extension to decentralized networks with limited local connectivity remains largely unexplored. This paper introduces \emph{topological secure aggregation} (TSA), which studies one-shot, information-theoretically secure aggregation of neighboring users' inputs over arbitrary network topologies. We develop a unified linear design framework that characterizes TSA achievability through the spectral properties of the communication graph, specifically the kernel of a diagonally modulated adjacency matrix. For several representative classes of $d$-regular graphs including ring, prism and complete topologies, we establish the optimal communication and secret key rate region. In particular, to securely compute one symbol of the neighborhood sum, each user must (i) store at least one key symbol, (ii) broadcast at least one message symbol, and (iii) collectively, all users must hold at least $d$ i.i.d. key symbols. Notably, this total key requirement depends only on the \emph{neighborhood size} $d$, independent of the network size, revealing a fundamental limit of SA in decentralized networks with limited local connectivity.

In decentralized federated learning (FL), multiple clients collaboratively learn a shared machine learning (ML) model by leveraging their privately held datasets distributed across the network, through interactive exchange of intermediate model updates. To ensure data security, cryptographic techniques are commonly employed to protect model updates during aggregation. Despite growing interest in secure aggregation, existing works predominantly focus on protocol design and computational guarantees, with limited understanding of the fundamental information-theoretic limits of such systems. Moreover, optimal bounds on communication and key usage remain unknown in decentralized settings, where no central aggregator is available. Motivated by these gaps, we study the problem of decentralized secure aggregation (DSA) from an information-theoretic perspective. Specifically, we consider a network ofKfully-connected users, each holding a private input—an abstraction of local training data—who aim to securely compute the sum of all inputs. The security constraint requires that no user learns anything beyond the input sum, even when colluding with up toTother users. We characterize the optimal rate region, which specifies the minimum achievable communication and secret key rates for DSA. In particular, we show that to securely compute one symbol of the desired input sum, each user must (i) transmit at least one symbol to others, (ii) hold at least one symbol of secret key, and (iii) all users must collectively hold no fewer thanK−1independent key symbols. Our results establish the fundamental performance limits of DSA, providing insights for the design of provably secure and communication-efficient protocols in decentralized learning.

Secure aggregation is concerned with the task of securely computing the sum of the inputs from multiple users by an aggregation server without letting the server know the inputs beyond their summation. It finds broad applications in distributed machine learning paradigms such as federated learning (FL) where numerous clients, each holding a proprietary dataset, periodically upload their locally trained models (abstracted as inputs) to a parameter server. The server then generates an aggregate model, typically through averaging, which is shared back with clients as the starting point for a new round of local training. To protect data security, secure aggregation protocols leverage cryptographic techniques to ensure the server gains no additional information beyond the input sum, even if it colludes with a subset of users. While the simple star client-server architecture provides insights into the fundamental utility-security trade-off in secure aggregation, it falls short of capturing the impact of network topology in practical systems. Motivated by hierarchical federated learning, we investigate the secure aggregation problem in a three-layer hierarchical network, where clustered users communicate with an aggregation server via an intermediate layer of relays. In addition to conventional server security which ensures the server learns only the input sum, we also impose relay security, requiring that the relays remain oblivious to users’ inputs. For such a hierarchical secure aggregation (HSA) problem, we characterize the optimal multifaceted trade-off between communication efficiency (measured by user-to-relay and relay-to-server communication rates) and key generation efficiency (including individual and source key rates). A core contribution of this work is the derivation of the optimal source key rate as a function of the number of relays, cluster size, and collusion level. We propose an optimal communication scheme alongside a key generation scheme utilizing a novel matrix structure called extended Vandermonde matrix that guarantees both input sum recovery and security. Moreover, we derive a tight information-theoretic converse proof to establish the optimal rate region for the HSA problem.

IEEE 802.11ax introduces orthogonal frequency division multiple access (OFDMA) to WiFi to support concurrent transmissions to a larger number of users. As bandwidth continues to grow, WiFi channels exhibit increased frequency selectivity, which poses new challenges for MU-MIMO user selection: the optimal user set varies across frequency and is interleaved over subbands (called resource units, or RUs). This frequency selectivity, coupled with the complex subband allocation pattern, renders conventional narrowband user selection algorithms inefficient for 802.11ax. In this paper, we propose ProxySelect, a scalable and frequency selectivity-aware user scheduling algorithm for joint OFDMA and MU-MIMO usage in 802.11ax under zero-forcing beamforming (ZFBF). The scheduling task is formulated as an integer linear program (ILP) with binary variables indicating user (group)-RU associations, and linear constraints ensuring standard compatibility. To reduce complexity, we introduce a novel proxy rate–a function of individual channel strengths and their correlations–that approximates the ZFBF rate without requiring cubic-complexity matrix inversion. Additionally, we develop a sampling-based candidate group generation scheme that selects up to T near-orthogonal user groups for each RU, thereby bounding the ILP size and ensuring scalability. Simulations using realistic ray-tracing-based channel models show that ProxySelect achieves near-optimal rate performance with significantly lower complexity.

In the problem of conditional disclosure of secrets (CDS), two parties, Alice and Bob, each has an input and shares a common secret. Their goal is to reveal the secret to a third party, Carol, as efficiently as possible, only if the inputs of Alice and Bob satisfy a certain functional relation$f$. To prevent leakage of the secret to Carol when the input combination is unqualified, both Alice and Bob introduce noise. This work aims to determine the noise capacity, defined as the maximum number of secret bits that can be securely revealed to Carol, normalized by the total number of independent noise bits held jointly by Alice and Bob. Our contributions are twofold. First, we establish the necessary and sufficient conditions under which the CDS noise capacity attains its maximum value of 1. Second, in addition to the above best-case scenarios, we derive an upper bound on the linear noise capacity for any CDS instance. In particular, this upper bound is equal to$(\rho-1)(d-1) /(\rho d-1)$, where$\rho$is the covering parameter of the graph representation of$f$, and$d$is the number of unqualified edges in residing unqualified path.

Motivated by federated learning (FL), secure aggregation (SA) aims to securely compute, as efficiently as possible, the sum of a set of inputs distributed across many users. To understand the impact of network topology, hierarchical secure aggregation (HSA) investigated the communication and secret key generation efficiency in a 3-layer relay network, where clusters of users are connected to the aggregation server through an intermediate layer of relays. Due to the pre-aggregation of the messages at the relays, HSA reduces the communication burden on the relay-to-server links and is able to support a large number of users. However, as the number of users increases, a practical challenge arises from heterogeneous security requirements–for example, users in different clusters may require varying levels of input protection. Motivated by this, we study weakly-secure HSA (WS-HSA) with collusion resilience, where instead of protecting all the inputs from any set of colluding users, only the inputs belonging to a predefined collection of user groups (referred to as security input sets) need to be protected against another predefined collection of user groups (referred to as collusion sets). Since the security input sets and collusion sets can be arbitrarily defined, our formulation offers a flexible framework for addressing heterogeneous security requirements in HSA. We characterize the optimal total key rate, i.e., the total number of independent key symbols required to ensure both server and relay security, for a broad range of parameter configurations. For the remaining cases, we establish lower and upper bounds on the optimal key rate, providing constant-factor gap optimality guarantees.

In the typical radio frequency (RF)-based wireless power transfer (WPT) system, the wireless power station (WPS) connected to the grid transmits energy to charge low-power sensors via radio signals. Such a system may not be green and also difficult to deploy in some special areas including deserts and mountainous areas, because it depends on the grid. To achieve a green RF WPT system design, this paper considers that the WPS is powered by natural energy sources rather than the grid. To explore the maximal total amount of the energy that can be harvested by the sensors, we focus on the offline setting, so similar to many existing works on offline optimization, we assume that the WPS knows prior knowledge about energy arrivals and channel changes, and then formulate an optimization problem to maximize the total harvested energy via optimizing the WPS’s time-domain transmit power subject to multiple constraints, including the finite battery capacity at the WPS, the causal relationship between the natural energy harvesting and the WPT, and the transmit power budget of the WPS, where for practicality, the nonlinear energy harvesting (EH) model is also taken into account. To solve this non-convex problem, we first equivalently transform it by using the epigraph reformulation and the variable substitution, and then use the first-order Taylor expansion to get an approximate convex version. Then, we present a successive convex approximation (SCA)-based algorithm to improve the accuracy of the obtained solution for approaching the optimal one. For the special case with a single sensor, we further propose a branch and bound (BB)-based algorithm that is able to get a more accurate solution with lower complexity than the SCA-based one. Numerical results demonstrate that the proposed algorithms are able to achieve the near-global optimal solution. As the average recharge rate increases, compared with the other two baselines, i.e., the greedy power (GP) policy and the constant power (CP) policy, the total harvested energy achieved by the SCA-based algorithm is up to about 2.48 times and 1.37 times that of the baselines respectively. For the single-sensor case, the BB-based algorithm always outperforms the SCA-based one in terms of the total harvested energy while reducing the running time required for solving by about 90% on average.

Secure aggregation is concerned with the task of securely uploading the inputs associated with multiple users to an aggregation server without revealing the user inputs to the server besides the summation of all inputs. It finds broad applications in distributed machine learning paradigms such as federated learning (FL). Motivated by practical hierarchical FL systems which utilize the client-edge-cloud network architecture to improve delay performance, we study the hierarchical secure aggregation (HSA) problem in a 3-layer hierarchical network where a total of$UV$users are connected to an aggregation server through$U$relay nodes each being associated with a disjoint subset of$V$users. Security requires that the server learn nothing beyond the desired sum of the inputs (server security), and each relay learn nothing about the user inputs (relay security) even if they collude with up to$T$users. We characterize the optimal communication and key rate region by proposing a novel secure aggregation scheme and deriving an information-theoretic converse that matches the achievable scheme. In particular, we show that when$T\geq(U-1)V$, the proposed HSA problem is infeasible. Otherwise when$T < (U-1)V$, to securely compute 1 bit of the desired sum, each user needs to upload at least 1 bit to its associating relay, each relay needs to upload at least 1 bit to the server, each user needs to hold at least 1 key bit, and all users need to collectively hold at least$\max\{V+T, \min\{U+T-1,UV- 1\}\}$(source) key bits. The characterization of the source key rate is a major contribution of this work.

This paper studies the high-speed railway mobile networks (HSRMN), where multiple railway-side sensors (RSs) are deployed along the track to sense environmental data, and multiple train-mounted sensors (TSs) are deployed on the train to collect train data. Both RSs and TSs are scheduled to transmit their sensed data respectively to the ground base station (BS) in a time division multiple access (TDMA) mode. To keep the data received at the BS from the RSs as fresh as possible and also ensure that the TSs complete the given uploading tasks, an optimization problem is established to minimize the average age of information (AoI) of the data gathered from RSs by jointly optimizing sensors’ scheduling and transmission power control constrained by the maximum transmission power budget of RSs and TSs. Since the problem is non-convex and lacks an explicit expression of the objective function and the prior information about future channel state, we present a deep Q-learning network (DQN)-based method to solve it. Particularly, the BS is viewed as the agent, and the action space is constructed by scheduling policy and power control. To further accelerate the convergence speed of the presented DQN-based solution framework, an action space-reduced (ASR) version of the DQN-based method, i.e., the ASR-DQN-based method, is designed by deriving a closed-form solution to the optimal transmission power for a given sensors’ scheduling policy. Numerical simulations show that, compared to the DQN-based method, the ASR-DQN-based method decreases the number of episodes required for convergence by about 23% and reduces the running time by about 41%. Moreover, compared with three baselines, i.e., the random method, the round-robin method, and the deep-Sarsa method, our presented ASR-DQN-based method achieves the lowest average AoI and has the best robustness among these compared methods.

We consider the cache-aided multiuser private information retrieval (MuPIR) problem with a focus on the special case of two messages, two users and arbitrary number of databases where the users have distinct demands of the messages. We characterize the optimal memory-load trade-off for the considered MuPIR problem by proposing a novel achievable scheme and a tight converse. The proposed achievable scheme uses the idea of cache-aided interference alignment (CIA) developed in the literature by the same authors. The proposed converse uses a tree-like decoding structure to incorporate both the decodability and privacy requirements of the users. While the optimal characterization of the cache-aided MuPIR problem is challenging in general, this work provides insight into understanding the general structure of the cache-aided MuPIR problem.

Elasticity is one important feature in modern cloud computing systems and can result in computation failure or significantly increase computing time. Such elasticity means that virtual machines over the cloud can be preempted under a short notice (e.g., hours or minutes) if a high-priority job appears; on the other hand, new virtual machines may become available over time to compensate the computing resources. Coded Storage Elastic Computing (CSEC) introduced by Yang et al. in 2018 is an effective and efficient approach to overcome the elasticity and it costs relatively less storage and computation load. However, one of the limitations of the CSEC is that it may only be applied to certain types of computations (e.g., linear) and may be challenging to be applied to more involved computations because the coded data storage and approximation are often needed. Hence, it may be preferred to use uncoded storage by directly copying data into the virtual machines. In addition, based on our own measurement, virtual machines on Amazon EC2 clusters often have heterogeneous computation speed even if they have exactly the same configurations (e.g., CPU, RAM, I/O cost). In this paper, we introduce a new optimization framework on Uncoded Storage Elastic Computing (USEC) systems with heterogeneous computing speed to minimize the overall computation time. Under this framework, we propose optimal solutions of USEC systems with or without straggler tolerance using different storage placements. Our proposed algorithms are evaluated using power iteration applications on Amazon EC2.

We propose using Carrier Sensing (CS) for distributed interference management in millimeter-wave (mmWave) cellular networks where spectrum is shared by multiple operators that do not coordinate among themselves. In addition, even the base station sites can be shared by the operators. We describe important challenges in using traditional CS in this setting and propose enhanced CS protocols to address these challenges. Using stochastic geometry, we develop a general framework for downlink coverage probability analysis of our shared mmWave network in the presence of CS and derive the downlink coverage probability expressions for several CS protocols. Our work is the first to investigate and analyze (using stochastic geometry) CS for mmWave networks with spectrum and BS sites shared among non-coordinating operators. We evaluate the downlink coverage probability of our shared mmWave network using simulations as well as numerical examples based on our analysis. Our evaluations show that our proposed approach leads to an improvement in coverage probability, compared to the coverage probability with no CS, for higher values of signal-to-interference and noise ratio (SINR). Interestingly, our evaluations also reveal that for lower values of SINR, not using any CS is the best strategy in terms of the downlink coverage probability.

This paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.

In the problem of cache-aided multiuser private information retrieval (MuPIR), a set of$K_{\mathrm{u}}$cache-equipped users wish to privately download a set of messages from$N$distributed databases each holding a library of$K$messages. The system works in two phases: the cache placement (prefetching) phase in which the users fill up their cache memory, and the private delivery phase in which the users' demands are revealed and they download an answer from each database so that the their desired messages can be recovered while each individual database learns nothing about the identities of the requested messages. The goal is to design the placement and the private delivery phases such that the load, which is defined as the total number of downloaded bits normalized by the message size, is minimized given any user memory size. This paper considers the MuPIR problem with two messages, arbitrary number of users and databases where uncoded prefetching is assumed, i.e., the users directly copy some bits from the library as their cached contents. We propose a novel MuPIR scheme inspired by the Maddah-Ali and Niesen (MAN) coded caching scheme. The proposed scheme achieves lower load than any existing schemes, especially the product design (PD), and is shown to be optimal within a factor of 8 in general and exactly optimal at very high or very low memory regimes.

We consider the problem of cache-aided Multiuser Private Information Retrieval (MuPIR) which is an extension of the single-user cache-aided PIR problem to the case of multiple users. In cache-aided MuPIR, each of the$K_{\mathrm{ u}}$cache-equipped users wishes to privately retrieve a message out of$K$messages from$N$databases each having access to the entire message library. Demand privacy requires that any individual database learns nothing about the demands of all users. The users are connected to each database via an error-free shared-link. In this paper, we aim to characterize the optimal trade-off between user cache memory and communication load for such systems. First, we propose a novel approach ofcache-aided interference alignment (CIA), for the MuPIR problem with$K=2$messages,$K_{\mathrm{ u}}=2$users and$N\ge 2$databases. The CIA approach is optimal when the cache placement is uncoded. For general cache placement, the CIA approach is optimal when$N=2$and 3 verified by the computer-aided converse approach. Second, for the general case, we propose aproduct design(PD) which incorporates the PIR code into the linear caching code. The product design is shown to be order optimal within a multiplicative factor of 8 and is exactly optimal in the high memory regime.

We consider a cache-aided interference network which consists of a library of N files, KTtransmitters and KRreceivers (users), each equipped with a local cache of size MTand MRfiles respectively, and connected via a discrete-time additive white Gaussian noise (AWGN) channel. Each receiver requests an arbitrary file from the library. The objective is to design a cache placement without knowing the receivers' requests and a communication scheme such that the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network model with one-shot transmission was firstly investigated by Naderializadeh et al., who proposed a scheme achieving an order-optimal one-shot sum-DoF of min {MTKT+KRMR/N, KR}. One of the biggest limitations of this scheme is the requirement of high subpacketizations. This paper attempts to design new algorithms to reduce the file subpacketization in such a network without hurting the sum-DoF. In particular, we propose a new approach for both prefetching and linearly coded delivery based on a combinatorial design called hypercube. The proposed approach reduces the subpacketization exponentially in terms of KRM/N ( M=MTor MRrepresents the transmitter/receiver cache size) and achieves the identical one-shot sum DoF when MTKT+KRMR/N ≤ KR.

This paper formulates the cache-aided multi-user Private Information Retrieval (MuPIR) problem, including Kucache-equipped users, each of which wishes to retrieve a desired message efficiently from N distributed databases with access to K independent messages. Privacy of the users’ demands requires that any individual database can not learn anything about the demands of the users. The load of this problem is defined as the average number of downloaded bits per desired message bit. The goal is to find the optimal memory-load trade-off while preserving the demand privacy. Besides the formulation of the MuPIR problem, the contribution of this paper is two-fold. First, we characterize the optimal memory-load trade-off for a system with N = 2 databases, K = 2 messages and Ku= 2 users demanding distinct messages; Second, a product design with order optimality guarantee is proposed. In addition, the product design can achieve the optimal load when the cache memory is large enough. The product design embeds the well-known Sun-Jafar PIR scheme into coded caching, in order to benefit from the coded caching gain while preserving the privacy of the users’ demands.

In this paper, we propose a new design framework on Device-to-Device (D2D) coded caching networks with optimal communication load (rate) but significantly less file subpacketizations compared to that of the well-known D2D coded caching scheme proposed by Ji, Caire and Molisch (JCM). The proposed design framework is referred to as the Packet Type-based (PTB) design, where each file is partitioned into packets according to their pre-defined types while the cache placement and user multicast grouping are based on the packet types. This leads to the so-called raw packet saving gain for the subpacketization levels. By a careful selection of transmitters within each multicasting group, a so-called further splitting ratio gain of the subpacketizatios can also be achieved. By the joint effect of the raw packet saving gain and the further splitting ratio gain, an order-wise subpacketization reduction can be achieved compared to the JCM scheme while preserving the optimal rate. In addition, as the first time presented in the literature according to our knowledge, we find that unequal subpacketizaton is a key to achieve subpacketization reductions when the number of users is odd. As a by-product, instead of directly translating shared link caching schemes to D2D caching schemes, at least for the sake of subpackeitzation, a new design framework is indeed needed.

We consider a cache-aided interference network which consists of a library of N files, KTtransmitters and KRreceivers (users), each equipped with a local cache of size MTand MRfiles respectively, and connected via a discrete-time additive white Gaussian noise channel. Each receiver requests an arbitrary file from the library. The objective is to design a cache placement without knowing the receivers' requests and a communication scheme such that the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network model has been investigated by Naderializadeh et al., who proposed a prefetching and a delivery scheme that achieve a sum-DoF of min{MTKT+ KRMR/N, KR}. One of the biggest limitations of this scheme is the requirement of high subpacketization level. This paper attempts to design new algorithms to reduce the file subpacketization in such a network. In particular, we propose a new approach for both prefetching and linear delivery based on a combinatorial design called hypercube. We show that the required number of packets per file can be exponentially reduced compared to the state-of-the-art scheme proposed by Naderializadeh et al., or the NMA scheme. When MTKT+ KRMR≤ KR, the achievable one-shot sum-DoF using this approach is MTKT+ KRMR/N, which shows that 1) the one-shot sum-DoF scales linearly with the aggregate cache size in the network and 2) it is within a factor of 2 to the information-theoretic optimum. Surprisingly, the identical and near optimal sum-DoF performance can be achieved using the hypercube approach with a much less file subpacketization.