Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.14723 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909083368423424 |
|---|---|
| author | Guo, Tao Guo, Laigang Xu, Yinfei Li, Congduan Jin, Shi Yeung, Raymond |
| author_facet | Guo, Tao Guo, Laigang Xu, Yinfei Li, Congduan Jin, Shi Yeung, Raymond |
| contents | Symmetric multilevel diversity coding (SMDC) is a source coding problem where the independent sources are ordered according to their importance. It was shown that separately encoding independent sources (referred to as ``\textit{superposition coding}") is optimal. In this paper, we consider an $(L,s)$ \textit{sliding secure} SMDC problem with security priority, where each source $X_α~(s\leq α\leq L)$ is kept perfectly secure if no more than $α-s$ encoders are accessible. The reconstruction requirements of the $L$ sources are the same as classical SMDC. A special case of an $(L,s)$ sliding secure SMDC problem that the first $s-1$ sources are constants is called the $(L,s)$ \textit{multilevel secret sharing} problem. For $s=1$, the two problems coincide, and we show that superposition coding is optimal. The rate regions for the $(3,2)$ problems are characterized. It is shown that superposition coding is suboptimal for both problems. The main idea that joint encoding can reduce coding rates is that we can use the previous source $X_{α-1}$ as the secret key of $X_α$. Based on this idea, we propose a coding scheme that achieves the minimum sum rate of the general $(L,s)$ multilevel secret sharing problem. Moreover, superposition coding of the $s$ sets of sources $X_1$, $X_2$, $\cdots$, $X_{s-1}$, $(X_s, X_{s+1}, \cdots, X_L)$ achieves the minimum sum rate of the general sliding secure SMDC problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sliding Secure Symmetric Multilevel Diversity Coding Guo, Tao Guo, Laigang Xu, Yinfei Li, Congduan Jin, Shi Yeung, Raymond Information Theory Symmetric multilevel diversity coding (SMDC) is a source coding problem where the independent sources are ordered according to their importance. It was shown that separately encoding independent sources (referred to as ``\textit{superposition coding}") is optimal. In this paper, we consider an $(L,s)$ \textit{sliding secure} SMDC problem with security priority, where each source $X_α~(s\leq α\leq L)$ is kept perfectly secure if no more than $α-s$ encoders are accessible. The reconstruction requirements of the $L$ sources are the same as classical SMDC. A special case of an $(L,s)$ sliding secure SMDC problem that the first $s-1$ sources are constants is called the $(L,s)$ \textit{multilevel secret sharing} problem. For $s=1$, the two problems coincide, and we show that superposition coding is optimal. The rate regions for the $(3,2)$ problems are characterized. It is shown that superposition coding is suboptimal for both problems. The main idea that joint encoding can reduce coding rates is that we can use the previous source $X_{α-1}$ as the secret key of $X_α$. Based on this idea, we propose a coding scheme that achieves the minimum sum rate of the general $(L,s)$ multilevel secret sharing problem. Moreover, superposition coding of the $s$ sets of sources $X_1$, $X_2$, $\cdots$, $X_{s-1}$, $(X_s, X_{s+1}, \cdots, X_L)$ achieves the minimum sum rate of the general sliding secure SMDC problem. |
| title | Sliding Secure Symmetric Multilevel Diversity Coding |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.14723 |