Markov-Enforced Discrete Diffusion Model for Digital Semantic Symbol Error Correction

TL;DR

This paper introduces SSCDM, a novel Markov-enforced discrete diffusion model that improves semantic symbol error correction in noisy channels by integrating continuous-time Markov chain solutions and topology-preserving codebook learning.

Contribution

The paper proposes a new diffusion model for digital semantic symbols that incorporates Markov chain theory and a topology-preserving codebook to enhance robustness in noisy transmission.

Findings

Significantly improves image reconstruction quality under low SNR.

Outperforms previous symbol-level denoising techniques.

Effective across different datasets.

Abstract

Diffusion models (DMs) have achieved remarkable success across various domains owing to their strong generative and denoising capabilities. Meanwhile, semantic communication based on neural joint source-channel coding (JSCC) has emerged as a promising paradigm for robust and efficient image transmission. However, severe channel noise can still distort the transmitted semantic symbols, resulting in significant performance degradation. Applying DMs to digital semantic symbols, particularly in vector quantization (VQ)-based systems, is fundamentally challenging because the Markov assumption does not hold for the symbol transition dynamics. To address this issue, we introduce SSCDM, a semantic symbol correcting diffusion model whose discrete-time transition dynamics are constructed using solutions from continuous-time Markov chain theory. Furthermore, to promote synergy between DMs and JSCC, our DM structure embeds discrete symbols into a latent feature space using a learned VQ codebook, and a self-organizing map-based loss is incorporated during codebook learning to enhance the geometric vicinity between neighboring digital symbols, thereby promoting topology-preserving semantic representations. Experimental results show that the proposed method significantly improves image reconstruction quality and outperforms previous symbol-level denoising techniques under low signal-to-noise ratio scenarios and different datasets.