Secure Symmetrical Multilevel Diversity Coding

Abstract

Secure symmetrical multilevel diversity coding (S-SMDC) is a source coding problem, where a total of L - N discrete memoryless sources (S1,...,S_L-N) are to be encoded by a total of L encoders. This thesis considers a natural generalization of SMDC to the secure communication setting with an additional eavesdropper. In a general S-SMDC system, a legitimate receiver and an eavesdropper have access to a subset U and A of the encoder outputs, respectively. Which subsets U and A will materialize are unknown a priori at the encoders. No matter which subsets U and A actually occur, the sources (S1,...,Sk) need to be perfectly reconstructable at the legitimate receiver whenever |U| = N +k, and all sources (S1,...,S_L-N) need to be kept perfectly secure from the eavesdropper as long as |A| <= N. A precise characterization of the entire admissible rate region is established via a connection to the problem of secure coding over a three-layer wiretap network and utilizing some properties of basic polyhedral structure of the admissible rate region. Building on this result, it is then shown that superposition coding remains optimal in terms of achieving the minimum sum rate for the general secure SMDC problem.