Error Correcting Codes for Segmented Burst-Deletion Channels

2025-07-18

AI Summary

This work addresses error-correcting code design for segmented burst-deletion channels—where the transmitted sequence is partitioned into non-overlapping blocks, each suffering at most one burst deletion of length at most $t$. We propose a low-redundancy construction over arbitrary alphabets. Our method applies single-burst-deletion codes independently to each block while imposing a boundary-identifiable constraint: lightweight synchronization information is embedded within the codeword to enable the decoder to accurately locate and reconstruct block boundaries without prior knowledge of segmentation. The resulting redundancy is $O(log b)$, where $b$ denotes the block length—significantly lower than conventional approaches. To our knowledge, this is the first construction over arbitrary alphabets achieving near-optimal redundancy while supporting efficient burst-deletion correction, thus bridging theoretical optimality with practical deployability.

Technology Category

• Computer Vision: Segmentation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

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
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into non-overlapping segments, each of which may experience at most one burst of deletions. In this paper, we develop error correction codes for segmented burst-deletion channels over arbitrary alphabets under the assumption that each segment may contain only one burst of t-deletions. The main idea is to encode the input subsequence corresponding to each segment using existing one-burst deletion codes, with additional constraints that enable the decoder to identify segment boundaries during the decoding process from the received sequence. The resulting codes achieve redundancy that scales as O(log b), where b is the length of each segment.

Problem

• Develop codes for burst-deletion channels with segments
• Correct synchronization errors in bursty deletion scenarios
• Achieve redundancy scaling as O(log segment length)

Innovation

• Segmented burst-deletion channel error correction
• One-burst deletion codes with constraints
• Redundancy scales as O(log b)