Asymptotically Optimal Codes for $(t,s)$-Burst Error

2024-03-18

AI Summary

研究针对(t,s)-突发错误，即连续删除与插入，提出近最优编码方法，使用log n + O(1)位纠正错误，适用于DNA存储等技术，同时优化了连续删除错误的处理。

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• 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
• Security and Privacy: Large-scale security measurements

Abstract

Recently, codes for correcting a burst of errors have attracted significant attention. One of the most important reasons is that bursts of errors occur in certain emerging techniques, such as DNA storage. In this paper, we investigate a type of error, called a $(t,s)$-burst, which deletes $t$ consecutive symbols and inserts $s$ arbitrary symbols at the same coordinate. Note that a $(t,s)$-burst error can be seen as a generalization of a burst of insertions ($t=0$), a burst of deletions ($s=0$), and a burst of substitutions ($t=s$). Our main contribution is to give explicit constructions of $q$-ary $(t,s)$-burst correcting codes with $log n + O(1)$ bits of redundancy for any given constant non-negative integers $t$, $s$, and $q geq 2$. These codes have optimal redundancy up to an additive constant. Furthermore, we apply our $(t,s)$-burst correcting codes to combat other various types of errors and improve the corresponding results. In particular, one of our byproducts is a permutation code capable of correcting a burst of $t$ stable deletions with $log n + O(1)$ bits of redundancy, which is optimal up to an additive constant.

Problem

• Error Correction
• DNA Storage
• Insertion-Deletion Codes

Innovation

• Error-Correction
• Efficient-Encoding
• Burst-Errors