An erasure broadcast network is considered with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. Lower and upper bounds are presented on the capacity-memory tradeoff of this network (the largest rate at which messages can be reliably communicated for given cache sizes). The lower bound is achieved by means of a joint cache-channel coding scheme and significantly improves over traditional schemes based on the separate cache-channel coding . In particular, it is shown that the joint cache-channel coding offers new global caching gains that scale with the number of strong receivers in the network. The upper bound uses bounding techniques from degraded broadcast channels and introduces an averaging argument to capture the fact that the contents of the cache memories are designed before knowing users’ demands. The derived upper bound is valid for all stochastically degraded broadcast channels. The lower and upper bounds match for a single weak receiver (and any number of strong receivers) when the cache size does not exceed a certain threshold. Improved bounds are presented for the special case of a single weak and a single strong receiver with two files and the bounds are shown to match over a large range of cache sizes.

Noisy Broadcast Networks With Receiver Caching

To process and transfer large amounts of data in emerging wireless services, it has become increasingly appealing to exploit distributed data communication and learning. Specifically, edge learning (EL) enables local model training on geographically disperse edge nodes and minimizes the need for frequent data exchange. However, the current design of separating EL deployment and communication optimization does not yet reap the promised benefits of distributed signal processing, and sometimes suffers from excessive signalling overhead, long processing delay, and unstable learning convergence. In this paper, we provide an overview on practical distributed EL techniques and their interplay with advanced communication optimization designs. In particular, typical performance metrics for dual-functional learning and communication networks are discussed. Also, recent achievements of enabling techniques for the dual-functional design are surveyed with exemplifications from the mutual perspectives of “communications for learning” and “learning for communications.” The application of EL techniques within a variety of future communication systems are also envisioned for beyond 5G (B5G) wireless networks. For the application in goal-oriented semantic communication, we present a first mathematical model of the goal-oriented source entropy as an optimization problem. In addition, from the viewpoint of information theory, we identify fundamental open problems of characterizing rate regions for communication networks supporting distributed learning-and-computing tasks. We also present technical challenges as well as emerging application opportunities in this field, with the aim of inspiring future research and promoting widespread developments of EL in B5G.

Edge Learning for B5G Networks With Distributed Signal Processing: Semantic Communication, Edge Computing, and Wireless Sensing

Distributed computing has become a common approach for large-scale computation tasks due to benefits such as high reliability, scalability, computation speed, and cost-effectiveness. However, distributed computing faces critical issues related to communication load and straggler effects. In particular, computing nodes need to exchange intermediate results with each other in order to calculate the final result, and this significantly increases communication overheads. Furthermore, a distributed computing network may include straggling nodes that run intermittently slower. This results in a longer overall time needed to execute the computation tasks, thereby limiting the performance of distributed computing. To address these issues, coded distributed computing (CDC), i.e., a combination of coding theoretic techniques and distributed computing, has been recently proposed as a promising solution. Coding theoretic techniques have proved effective in WiFi and cellular systems to deal with channel noise. Therefore, CDC may significantly reduce communication load, alleviate the effects of stragglers, provide fault-tolerance, privacy and security. In this survey, we first introduce the fundamentals of CDC, followed by basic CDC schemes. Then, we review and analyze a number of CDC approaches proposed to reduce the communication costs, mitigate the straggler effects, and guarantee privacy and security. Furthermore, we present and discuss applications of CDC in modern computer networks. Finally, we highlight important challenges and promising research directions related to CDC.

A Comprehensive Survey on Coded Distributed Computing: Fundamentals, Challenges, and Networking Applications

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the no feedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this paper. Examples of strictly essentially less-noisy BCs are the binary symmetric BC or the binary erasure BC with unequal crossover or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feedback quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme, the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme also applies to memoryless BCs without feedback but with strictly causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.

Coding Schemes With Rate-Limited Feedback That Improve Over the No Feedback Capacity for a Large Class of Broadcast Channels

We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean: • the channel matrices of the MAC and the BC are transposes of each other and

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MIMO MAC-BC Duality With Linear-Feedback Coding Schemes

We consider the K ≥ 2-user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk and Kailath's scheme for point-to-point channels or Ozarow and Leung's scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity C (which is the same with and without feedback). In the extreme case where the number of receivers K → ∞, the largest rate achieved by linear-feedback schemes with a message point tends to 0. To contrast this negative result, we describe a scheme for rate-limited feedback that uses the feedback in an intermittent way, i.e., the receivers send feedback signals only in few channel uses. This scheme achieves all rates R up to capacity C with an Lth order exponential decay of the probability of error if the feedback rate Rfb is at least (L - 1)R for some positive integer L.

Insufficiency of Linear-Feedback Schemes In Gaussian Broadcast Channels with Common Message

In this paper, we consider a two-layer caching-aided network, where a single server consisting of a library of N files connects with multiple relays, each equipped with a cache memory of M 1 files and each relay connects with a distinct set of users, each equipped with a cache memory of M 2 files. We design a caching scheme that exploits the spared transmission time resource by constructing a concurrent transmission between the two layers. It is shown that the caching scheme is order optimal and achieves an additive parallel gain compared to the previously known caching scheme. Also, we show that for the two-relay case, if each relay’s caching size M 1 equals to 0.382N, our scheme achieves the optimal delay as M 1 = N, implying that increasing the relay’s cache size will not always reduce the transmission delay.

Reduce Transmission Delay for Caching-Aided Two-Layer Networks

Federated learning (FL), as a disruptive machine learning (ML) paradigm, enables the collaborative training of a global model over decentralized local data sets without sharing them. It spans a wide scope of applications from the Internet of Things (IoT) to biomedical engineering and drug discovery. To support low-latency and high-privacy FL over wireless networks, in this article, we propose a reconfigurable intelligent surface (RIS)-empowered over-the-air FL system to alleviate the dilemma between learning accuracy and privacy. This is achieved by simultaneously exploiting the channel propagation reconfigurability with RIS for boosting the received signal power, as well as the waveform superposition property with over-the-air computation (AirComp) for fast model aggregation. By considering a practical scenario, where high-dimensional local model updates are transmitted across multiple communication blocks, we characterize the convergence behaviors of the differentially private federated optimization algorithm. We further formulate a system optimization problem to optimize the learning accuracy while satisfying privacy and power constraints via the joint design of transmit power, artificial noise, and phase shifts at RIS, for which a two-step alternating minimization framework is developed. Simulation results validate our systematic, theoretical, and algorithmic achievements and demonstrate that RIS can achieve a better tradeoff between privacy and accuracy for over-the-air FL systems.

Differentially Private Federated Learning via Reconfigurable Intelligent Surface

We consider the $K\geq 2$-user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk & Kailath's scheme for point-to-point channels or Ozarow & Leung's scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity $C$ (which is the same with and without feedback). In the extreme case where the number of receivers $K\to \infty$, the largest rate achieved by linear-feedback schemes with a message point tends to 0. 
To contrast this negative result, we describe a scheme for \emph{rate-limited} feedback that uses the feedback in an intermittent way, i.e., the receivers send feedback signals only in few channel uses. This scheme achieves all rates $R$ up to capacity $C$ with an $L$-th order exponential decay of the probability of error if the feedback rate $R_{\textnormal{fb}}$ is at least $(L-1)R$ for some positive integer $L$.

We propose two coding schemes for discrete memoryless broadcast channels (DMBCs) with rate-limited feedback In our first scheme, the encoder does not process the feedback information that it receives, but simply relays it to the other receiver This first scheme shows that arbitrary small, but positive, feedback rate suffices to improve over the nofeedback capacity for many DMBCs such as: any binary erasure BC (BEBC) with unequal erasure probability at the two receivers, any binary symmetric BC (BSBC) with unequal crossover probability at the receivers, and any binary erasure/binary symmetric BC (BEC/BSC-BC) with nonequal single-user capacity to the receivers The scheme also improves the entire nofeedback capacity region for any strictly essentially less-noisy BC–a new class of BCs introduced in this paper–that is not physically degraded In our second scheme, the encoder decodes all the feedback information and processes it with some local information before sending the result to the receivers For some setups, this second scheme performs better than our first scheme In the limit, as the available feedback-rates tend to infinity, our second scheme coincides with a special case of the Shayevitz and Wigger (SW) scheme for DMBCs with generalized feedback The mentioned special case of the SW-scheme includes several other schemes as further special cases, eg, the schemes by Dueck and by MaddahAli and Tse which achieve capacity or the degrees of freedom on the respectively studied channels All our results hold also with noisy feedback when the receivers can code over the feedback links

Youlong Wu

Papers

Insufficiency of Linear-Feedback Schemes In Gaussian Broadcast Channels with Common Message

Reduce Transmission Delay for Caching-Aided Two-Layer Networks

Differentially Private Federated Learning via Reconfigurable Intelligent Surface

Insufficiency of Linear-Feedback Schemes In Gaussian Broadcast Channels with Common Message

Coding schemes for discrete memoryless broadcast channels with rate-limited feedback