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In recent years, semantic communication has received significant attention from both academia and industry, driven by the growing demands for ultra-low latency and high-throughput capabilities in emerging intelligent services. Nonetheless, a comprehensive and effective theoretical framework for semantic communication has yet to be established. In particular, finding the fundamental limits of semantic communication, exploring the capabilities of semantic-aware networks, or utilizing theoretical guidance for deep learning in semantic communication are very important yet still unresolved issues. In general, the mathematical theory of semantic communication and the mathematical representation of semantics are referred to as semantic information theory. In this paper, we introduce the pertinent advancements in semantic information theory. Grounded in the foundational work of Claude Shannon, we present the latest developments in semantic entropy, semantic rate-distortion, and semantic channel capacity. Additionally, we analyze some open problems in semantic information measurement and semantic coding, providing a theoretical basis for the design of a semantic communication system. Furthermore, we carefully review several mathematical theories and tools and evaluate their applicability in the context of semantic communication. Finally, we shed light on the challenges encountered in both semantic communication and semantic information theory.

As a promising distributed learning paradigm, federated learning (FL) faces the challenge of communication–computation bottlenecks in practical deployments. In this work, we mainly focus on the pruning, quantization, and coding of FL. By adopting a layer-wise operation, we propose an explicit and universal scheme: FedLP-Q (federated learning with layer-wise pruning-quantization). Pruning strategies for homogeneity/heterogeneity scenarios, the stochastic quantization rule, and the corresponding coding scheme were developed. Both theoretical and experimental evaluations suggest that FedLP-Q improves the system efficiency of communication and computation with controllable performance degradation. The key novelty of FedLP-Q is that it serves as a joint pruning-quantization FL framework with layer-wise processing and can easily be applied in practical FL systems. © 2023 by the authors.

This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is (Formula presented.). Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition (Formula presented.) of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images. © 2022 by the authors.

In this letter, we propose soft compression, an lossless compression approach to shape coding for images using location index and codebook of designed shapes with various sizes. This method is different from traditional image compression methods, as it aims at finding the basic shape blocks of pictures to improve the compression ratio from the perspective of information theory and frequency. In particular, the triplets including location and codeword are stored when encoding an image instead of the entire array. It is shown that soft compression can greatly reduce the bandwidth and storage space needed in the process of transmitting and storing the same kind of images.

In this letter, we propose soft compression, an lossless compression approach to shape coding for images using location index and codebook of designed shapes with various sizes. This method is different from traditional image compression methods, as it aims at finding the basic shape blocks of pictures to improve the compression ratio from the perspective of information theory and frequency. In particular, the triplets including location and codeword are stored when encoding an image instead of the entire array. It is shown that soft compression can greatly reduce the bandwidth and storage space needed in the process of transmitting and storing the same kind of images.