FR3.R2.2

Sliding Secure Symmetric Multilevel Diversity Coding

Tao Guo, Southeast University, China; Laigang Guo, Beijing Normal University, China; Yinfei Xu, Southeast University, China; Congduan Li, Sun Yat-sen University, China; Shi Jin, Southeast University, China; Raymond W. Yeung, The Chinese University of Hong Kong, Hong Kong SAR of China

Session:
Network Information Theory 2

Track:
7: Network Information Theory

Location:
Ypsilon I-II-III

Presentation Time:
Fri, 12 Jul, 14:55 - 15:15

Session Chair:
Michael Gastpar, EPFL
Abstract
Symmetric multilevel diversity coding (SMDC) is a multi-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, an $(L,s)$ sliding secure SMDC problem is considered, where $L$ is the number of encoders and $s$ is the security threshold, which means that each source $\bm{X}_{\alpha}$ is kept perfectly secure if no more than $\alpha-s$ encoders are accessible. It is shown that superposition coding is optimal for $s=1$. The rate region for $(L,s)=(3,2)$ is characterized, which implies the suboptimality of superposition coding for the general problem. The main idea that joint coding can reduce rates is that we can use the previous source $\bm{X}_{\alpha-1}$ as the secret key of $\bm{X}_{\alpha}$. Based on this idea, a pseudo-superposition coding scheme is proposed to achieve the minimum sum rate, which uses superposition for the $s$ sets of sources $\bm{X}_1$, $\bm{X}_2$, $\cdots$, $\bm{X}_{s-1}$, $(\bm{X}_s, \bm{X}_{s+1}, \cdots, \bm{X}_L)$ and joint encoding among $\bm{X}_s, \bm{X}_{s+1}, \cdots, \bm{X}_L$.
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