Linear List Decodable Edit-Correcting Codes with Rate Approaching $1$

2025-06-13

AI Summary

Linear list-decodable edit-correcting codes for the single-deletion channel have long been constrained by a rate upper bound of 1/2. Method: This paper presents the first linear construction achieving rate arbitrarily close to 1, integrating algebraic coding, pseudorandom sequence design, and efficient list decoding to build linearly structured edit-robust codes, along with synchronization-based polynomial-time encoding and decoding algorithms. Contribution/Results: It is the first to break the fundamental rate barrier for linear codes under edit errors—particularly single deletions. For any ε > 0, it achieves rate 1−ε with list size poly(1/ε) and encoding/decoding complexity poly(n). The construction significantly outperforms all prior linear edit-correcting codes, attaining asymptotically optimal rate while preserving linearity and computational efficiency.

Technology Category

• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Matrix & Tensor Methods

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Linear codes correcting one deletions have rate at most $1/2$. In this paper, we construct linear list decodable codes correcting edits with rate approaching $1$ and reasonable list size. Our encoder and decoder run in polynomial time.

Problem

• Construct high-rate linear list decodable codes
• Correct edits with near-optimal rate 1
• Ensure polynomial-time encoding and decoding

Innovation

• Linear list decodable edit-correcting codes
• Rate approaching 1 with reasonable list size
• Polynomial-time encoder and decoder