TopoCode: Topologically Informed Error Detection and Correction in Communication Systems

TL;DR

TopoCode introduces a novel topologically informed error detection and correction method using Topological Data Analysis, enhancing message-level data integrity in high-data-rate, low-latency communication systems like XR and holography.

Contribution

It applies Topological Data Analysis and persistent homology to encode topological features for message-level error correction with minimal redundancy.

Findings

Effective in low SNR conditions

Reduces redundancy compared to traditional codes

Improves message integrity in high-data-rate systems

Abstract

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.