Secure successive refinement with degraded side information

In this paper, we investigate the problem of successive refinement with side information (SI) under secrecy constraint. In particular, under classical successive refinement coding scheme, there are degraded SI sequences Yⁿ and Zⁿ at two decoders and Eⁿ at the eavesdropper. Based on the status of two switches, three different cases are investigated. In case 1 and 3, the eavesdropper only observes output of encoder 1 and 2, respectively, while in case 2, the eavesdropper observes outputs of both encoder 1 and 2. The Markov chain X - Y - (Z, E) holds in all cases. The equivocation is measured by the normalized entropy of source sequence conditioned on the observation of eavesdropper. We completely characterize the rate-distortion-equivocation regions for all three cases, and show that layered coding is optimal. Finally, a binary source example is given.