Traditional error detection and correction codes focus on bit-level fidelity, which is insufficient for emerging technologies like eXtended Reality (XR) and holographic communications requiring high-data-rate, low-latency systems. Bit-level metrics cannot comprehensively evaluate Quality-of-Service (QoS) in these scenarios. This letter proposes TopoCode which leverages Topological Data Analysis (TDA) and persistent homology to encode topological information for message-level error detection and correction. It introduces minimal redundancy while enabling effective data reconstruction, especially in low Signal-to-Noise Ratio (SNR) conditions. TopoCode offers a promising approach to meet the demands of next-generation communication systems prioritizing semantic accuracy and message-level integrity.

翻译：传统的错误检测与校正码主要关注比特级保真度，这对于扩展现实（XR）和全息通信等需要高数据速率、低延迟系统的新兴技术而言已显不足。在这些场景中，比特级指标无法全面评估服务质量（QoS）。本文提出TopoCode，该方法利用拓扑数据分析（TDA）和持续同调，对拓扑信息进行编码以实现消息级的错误检测与校正。它在引入最小冗余的同时，实现了有效的数据重建，尤其是在低信噪比（SNR）条件下。TopoCode为满足下一代通信系统对语义准确性和消息级完整性的需求提供了一种前景广阔的方法。