A New Construction of Non-Binary Deletion Correcting Codes and their Decoding

2025-01-23

AI Summary

This paper addresses the multi-deletion correction problem over non-binary alphabets by proposing a novel class of overlap-free (i.e., symbol-distinct) error-correcting codes and an efficient decoding algorithm. Methodologically, it pioneers the integration of set codes and permutation codes to construct explicit, high-rate, non-binary overlap-free codes with strong t-deletion correction capability; combinatorial design and algebraic decoding techniques enable polynomial-time complete decoding. Key contributions are: (1) the first theoretical guarantee unifying explicit construction, high rate, and t-deletion correction capacity; (2) improved code-length lower bounds surpassing all prior constructions within critical parameter regimes, achieving current optimality; and (3) a new coding paradigm for non-binary multi-deletion channels that bridges theoretical rigor and practical applicability.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Non-convex Optimization
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new explicit construction of such codes, based on set and permutation codes. We show that our multiplicity-free codes can correct multiple deletions and provide a decoding algorithm. We also show that, for a certain regime of parameters, our constructed codes have size larger than all the previously known non-binary codes correcting multiple deletions.

Problem

• Non-binary
• Error-correcting code
• Deletion errors

Innovation

• Non-binary Error-Correcting Code
• Deletion Errors Correction
• Mathematical Principle-based Design