Polar Code Based Federated Learning: Convergence Analysis and Resource Allocation

Personalized federated learning (PFL) is a promising paradigm for collaborative learning over distributed devices, where edge nodes collaboratively train personalized models without sharing raw data. Although PFL addresses data heterogeneity by learning client-specific models, it still suffers from substantial uplink and downlink communication costs when exchanging high-dimensional parameters in bandwidth-constrained systems. Recent one-bit methods achieve extreme compression, but they usually rely on a single thresholding rule applied to the whole model. This design has two limitations. First, it overlooks layer-wise differences in parameter distributions and quantization sensitivities. Second, a single threshold provides only coarse binary information and cannot capture fine-grained variations in parameter distributions. To address these issues, we propose a communication-efficient PFL framework via layer-wise multi-threshold random sketching. In the proposed method, each layer is assigned its own set of quantization thresholds, so that the compressed representation can adapt to layer-specific statistics while using multiple intervals to provide a finer low-bit description of sketched parameters. The proposed method supports bidirectional communication using compact low-bit sketches and improves the communication-accuracy tradeoff compared with existing one-bit compression approaches.

Federated Learning (FL) has become a foundational paradigm for privacy-preserving distributed intelligence, yet its scalability remains fundamentally constrained by communication bottlenecks, device heterogeneity, and the challenges of training under statistically non-IID data. Quantization is one of the most effective mechanisms for mitigating these limitations, reducing both uplink/downlink payloads and on-device computation. This paper provides the first FL-centric systematic review of quantization, introducing a novel taxonomy organized around FL-specific dimensions, including client heterogeneity, aggregation consistency, communication-scheduling adaptation, non-IID robustness, privacy/security integration, and hardware/energy co-optimization. Beyond cataloging existing methods, we analyze how quantization interacts with core FL behaviors such as client drift, partial participation, convergence stability, secure aggregation, and differential privacy. We further identify cross-method insights, open research gaps, and design guidelines for practitioners deploying quantized FL on mobile, IoT, and edge platforms. This survey thus establishes quantization not merely as a compression technique, but as a fundamental systems component shaping the performance, robustness, and practicality of modern FL.

Quantum federated learning (QFL) combines the robust data processing of quantum computing with the privacy-preserving features of federated learning (FL). However, in large-scale wireless networks, optimizing sum-rate is crucial for unlocking the true potential of QFL, facilitating effective model sharing and aggregation as devices compete for limited bandwidth amid dynamic channel conditions and fluctuating power resources. This paper studies a novel sum-rate maximization problem within a muti-channel QFL framework, specifically designed for non-orthogonal multiple access (NOMA)-based large-scale wireless networks. We develop a sum-rate maximization problem by jointly considering quantum device's channel selection and transmit power. Our formulated problem is a non-convex, mixed-integer nonlinear programming (MINLP) challenge that remains non-deterministic polynomial time (NP)-hard even with specified channel selection parameters. The complexity of the problem motivates us to create an effective iterative optimization approach that utilizes the sophisticated quantum approximate optimization algorithm (QAOA) to derive high-quality approximate solutions. Additionally, our study presents the first theoretical exploration of QFL convergence properties under full device participation, rigorously analyzing real-world scenarios with nonconvex loss functions, diverse data distributions, and the effects of quantum shot noise. Extensive simulation results indicate that our multi-channel NOMA-based QFL framework enhances model training and convergence behavior, surpassing conventional algorithms in terms of accuracy and loss. Moreover, our quantum-centric joint optimization approach achieves more than a 100% increase in sum-rate while ensuring rapid convergence, significantly outperforming the state-of-the-arts.