A Theoretically-Grounded Codebook for Digital Semantic Communications
Lingyi Wang, Rashed Shelim, Walid Saad, Naren Ramakrishnan
TL;DR
The paper addresses the problem of efficiently and robustly discretizing high-dimensional semantic features for digital communications. It introduces an information-theoretic framework that ties synonymous semantic mappings to Voronoi-based quantization, derives mutual information between semantic features and discrete indices, and optimizes index usage via entropy regularization and channel-aware distortion losses. Key contributions include a unified theory connecting semantic mappings to codebook partitions, practical end-to-end losses that balance quantization fidelity, index entropy, and channel noise, and analysis of optimal codebook size under error-rate and bandwidth constraints; empirical results on image reconstruction show notable gains over prior VQ-VAE-based designs. Overall, the approach enhances quantization efficiency, transmission efficiency, and robustness in digital semantic communications, with tangible improvements demonstrated under realistic channel conditions.
Abstract
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.