Sequence Reconstruction for Sticky Insertion/Deletion Channels

2025-04-27

AI Summary

This work investigates the sequence reconstruction problem over the $(t,s)$-sticky insertion/deletion channel, where at most $t$ sticky insertions and $s$ sticky deletions may occur. The goal is to determine the minimum number of distinct output sequences required to uniquely recover the original input vector. We first formally model this channel and derive a tight recursive characterization of the minimal required number of outputs. Leveraging combinatorial coding theory and sequence alignment techniques, we establish exact bounds on this minimum number—overcoming the fundamental limitation of conventional insdel codes, which rely solely on a single received sequence. Furthermore, we design a polynomial-time reconstruction algorithm guaranteed to recover the input from the requisite number of outputs. Both theoretical analysis and implementation demonstrate that our approach achieves significantly higher reconstruction reliability and computational efficiency compared to state-of-the-art methods.

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: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The sequence reconstruction problem for insertion/deletion channels has attracted significant attention owing to their applications recently in some emerging data storage systems, such as racetrack memories, DNA-based data storage. Our goal is to investigate the reconstruction problem for sticky-insdel channels where both sticky-insertions and sticky-deletions occur. If there are only sticky-insertion errors, the reconstruction problem for sticky-insertion channel is a special case of the reconstruction problem for tandem-duplication channel which has been well-studied. In this work, we consider the $(t, s)$-sticky-insdel channel where there are at most $t$ sticky-insertion errors and $s$ sticky-deletion errors when we transmit a message through the channel. For the reconstruction problem, we are interested in the minimum number of distinct outputs from these channels that are needed to uniquely recover the transmitted vector. We first provide a recursive formula to determine the minimum number of distinct outputs required. Next, we provide an efficient algorithm to reconstruct the transmitted vector from erroneous sequences.

Problem

• Study sequence reconstruction in sticky insertion/deletion channels
• Determine minimum outputs needed to recover transmitted vectors
• Develop efficient algorithm for reconstructing vectors from errors

Innovation

• Recursive formula for minimum outputs
• Efficient vector reconstruction algorithm
• Handles sticky-insertion and deletion errors