Sliding Secure Symmetric Multilevel Diversity Coding

Tao Guo, Laigang Guo, Yinfei Xu, Congduan Li, Shi Jin, Raymond W. Yeung

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 sepa-rately encoding independent sources, referred to as 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 $X$ ais kept perfectly secure if no more than a - $s$ 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 X a -1 as the secret key of X a. 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 Xl, X2,‥ Xs-1, (Xs, Xs+1,”, XL). and joint encoding among Xs, Xs+1,”, XL.