论文标题
使用子包装的嵌入式索引代码构建
An Embedded Index Code Construction Using Sub-packetization
论文作者
论文摘要
索引编码问题（ICP）的一种变体，在[A. Porter和M. Wootter，“嵌入式索引编码”，ITW，瑞典，2019年]，这是由于其在分布式计算中的应用而激发的，每个用户都可以作为其他用户充当发送者，并报告了代码构建算法。构造取决于矩阵的微小兰器的计算，该矩阵在计算上是密集型的。在[A。 Mahesh，N。SageerKarat和B. S. Rajan，“嵌入式索引编码问题的最低级别”，ISIT，2020年]，对于EICP，引入了侧面信息矩阵的概念，证明了最佳量标准线性索引索引代码的长度等于侧面形式的最低范围。作者为EICP - \ textit {连续且对称嵌入式索引编码问题（CS -EICP）}提供了明确的代码构建。我们介绍了索引编码问题中消息子包装的想法，以与先前的工作中提供的标量线性解决方案相比，为CS-EICP提供了新颖的代码构建。对于CS-EICP，归一化速率定义为所有用户通过所有消息的位总数归一化的位数，因为我们的构造要比标量线性代码的Mahesh等人所达到的标准化率要小。
A variant of the index coding problem (ICP), the embedded index coding problem (EICP) was introduced in [A. Porter and M. Wootters, "Embedded index coding," ITW, Sweden, 2019] which was motivated by its application in distributed computing where every user can act as sender for other users and an algorithm for code construction was reported. The constructions depends on the computation of minrank of a matrix, which is computationally intensive. In [A. Mahesh, N. Sageer Karat and B. S. Rajan, "Min-rank of Embedded Index Coding Problems," ISIT, 2020], for EICP, a notion of side-information matrix was introduced and it was proved that the length of an optimal scalar linear index code is equal to the min-rank of the side-information matrix. The authors have provided an explicit code construction for a class of EICP - \textit{Consecutive and Symmetric Embedded Index Coding Problem (CS-EICP)}. We introduce the idea of sub-packetization of the messages in index coding problems to provide a novel code construction for CS-EICP in contrast to the scalar linear solutions provided in the prior works. For CS-EICP, the normalized rate, which is defined as the number of bits transmitted by all the users together normalized by the total number of bits of all the messages, for our construction is lesser than the normalized rate achieved by Mahesh et al.,for scalar linear codes.
