论文标题
单dionion单固体校正代码
Single-Deletion Single-Substitution Correcting Codes
论文作者
论文摘要
纠正插入/删除以及替换错误同时在基于DNA的存储系统以及经典通信中起着重要作用。本文介绍了构建可以纠正单个插入或删除以及单个替代的代码的基本任务。得出了对单删除单固体校正代码大小的非反应上限，这表明这种长度$ n $的冗余必须至少为$ 2 \ log n $。对二进制代码和非二进制代码均显示了界限，而单个删除的扩展为二进制代码进行了多个替换。得出了最多$ 6 \ log n + 8 $冗余位的单位单固体校正代码的明确构造。请注意，此问题最著名的构造必须使用3台式校正代码，其最著名的冗余大约为$ 24 \ log n $。
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that can correct a single insertion or deletion along with a single substitution. A non-asymptotic upper bound on the size of single-deletion single-substitution correcting codes is derived, showing that the redundancy of such a code of length $n$ has to be at least $2 \log n$. The bound is presented both for binary and non-binary codes while an extension to single deletion and multiple substitutions is presented for binary codes. An explicit construction of single-deletion single-substitution correcting codes with at most $6 \log n + 8$ redundancy bits is derived. Note that the best known construction for this problem has to use 3-deletion correcting codes whose best known redundancy is roughly $24 \log n$.
