Sequence Reconstruction under Channels with Multiple Bursts of Insertions or Deletions

2025-04-29

AI Summary

This work investigates the unique reconstruction of sequences corrupted by multi-burst insertion/deletion errors—each burst having identical length $b$—in multi-channel transmission, aiming to determine the minimum number of channels required for unambiguous reconstruction. We propose a unified framework integrating error-ball intersection analysis, combinatorial coding, and sequence distance construction. For multi-burst insertions, we derive the first closed-form expression for the minimum channel count. For multi-burst deletions, we establish tight upper and lower bounds and prove their asymptotic optimality under typical parameter regimes. By extending Levenshtein’s classical sequence reconstruction theory to burst-error models, our results provide a rigorous theoretical foundation and precise quantitative guidelines for designing redundancy-aware codes resilient to synchronization errors.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• 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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels required for the unique reconstruction of the transmitted sequence. Levenshtein established that this number exceeds the maximum size of the intersection between the error balls of any two distinct transmitted sequences by one. In this paper, we consider channels subject to multiple bursts of insertions and multiple bursts of deletions, respectively, where each burst has an exact length of value b. We provide a complete solution for the insertion case while partially addressing the deletion case.

Problem

• Study sequence reconstruction under multiple insertion/deletion bursts
• Determine minimum channels needed for unique sequence recovery
• Solve insertion case fully and deletion case partially

Innovation

• Multiple bursts of insertions and deletions
• Exact length b for each burst
• Complete solution for insertion case