The use of a learnable codebook provides an efficient way for semantic communications to map vector-based high-dimensional semantic features onto discrete symbol representations required in digital communication systems. In this paper, the problem of codebook-enabled quantization mapping for digital semantic communications is studied from the perspective of information theory. Particularly, a novel theoretically-grounded codebook design is proposed for jointly optimizing quantization efficiency, transmission efficiency, and robust performance. First, a formal equivalence is established between the one-to-many synonymous mapping defined in semantic information theory and the many-to-one quantization mapping based on the codebook's Voronoi partitions. Then, the mutual information between semantic features and their quantized indices is derived in order to maximize semantic information carried by discrete indices. To realize the semantic maximum in practice, an entropy-regularized quantization loss based on empirical estimation is introduced for end-to-end codebook training. Next, the physical channel-induced semantic distortion and the optimal codebook size for semantic communications are characterized under bit-flip errors and semantic distortion. To mitigate the semantic distortion caused by physical channel noise, a novel channel-aware semantic distortion loss is proposed. Simulation results on image reconstruction tasks demonstrate the superior performance of the proposed theoretically-grounded codebook that achieves a 24.1% improvement in peak signal-to-noise ratio (PSNR) and a 46.5% improvement in learned perceptual image patch similarity (LPIPS) compared to the existing codebook designs when the signal-to-noise ratio (SNR) is 10 dB.

翻译：在数字语义通信中，可学习码本的使用为将基于向量的高维语义特征映射到数字通信系统所需的离散符号表示提供了一种高效方法。本文从信息论的角度研究了数字语义通信中码本启用的量化映射问题。特别地，提出了一种新颖的、基于理论基础的码本设计，用于联合优化量化效率、传输效率和鲁棒性能。首先，建立了语义信息论中定义的一对多同义映射与基于码本Voronoi分区的多对一量化映射之间的形式等价关系。随后，推导了语义特征与其量化索引之间的互信息，以最大化离散索引所携带的语义信息。为实现实际中的语义信息最大化，引入了一种基于经验估计的熵正则化量化损失，用于码本的端到端训练。接下来，在比特翻转误差和语义失真条件下，刻画了物理信道引起的语义失真以及语义通信的最优码本大小。为减轻物理信道噪声引起的语义失真，提出了一种新颖的信道感知语义失真损失。在图像重建任务上的仿真结果表明，所提出的基于理论基础的码本性能优越，在信噪比为10 dB时，与现有码本设计相比，其峰值信噪比提升了24.1%，学习感知图像块相似度提升了46.5%。