一些q-ary代码的新构造,用于纠正最多一连串的删除
Wentu Song1, Kui Cai1, Tony Q S Quek1
1Science, Mathematics and Technology (SMT) Cluster, Singapore University of Technology and Design, Singapore 487372, Singapore.
Entropy (Basel, Switzerland)
|January 24, 2025
概括
这项研究引入了新的q-ary代码来纠正爆破删除. 新的结构为经典和重建错误纠正场景提供了较低的冗余性.
科学领域:
- 编码理论编码理论
- 信息理论 信息理论
- 计算机科学 计算机科学
背景情况:
- 突发删除在数据传输和存储方面带来了重大挑战.
- 现有的错误纠正代码通常在有效处理爆发错误方面存在局限性.
研究的目的:
- 构建新的q-ary代码,能够纠正一连串多达t次的删除.
- 在两个不同的错误纠正场景中为这些代码开发高效的编码和解码方法.
主要方法:
- 为突破删除纠正量身定制的q-ary代码的构建.
- 对两个场景的代码冗余性,编码复杂性和解码复杂性的分析:经典的错误纠正和重建代码.
- 开发明确编码功能的开发.
主要成果:
- 与现有工程相比,在经典 (log n + 8 log log n + o(log log n) 位) 和重建 (8 log log n + o(log log n) 位) 场景中实现了较低的冗余.
- 为这两种结构提供了高效的编码和解码复杂性.
- 开发了更简单的显式编码功能.
结论:
- 拟议的q-ary代码在冗余性方面提供了更好的性能,用于纠正突发删除.
- 新的结构对于单读和多读 (两个读) 错误纠正场景都是有效的.
- 提供了明确的编码功能,简化了实际实施.
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