Symmetrical multilevel diversity coding (SMDC) is a network compression problem introduced by Roche (1992) and Yeung (1995). In this setting, a simple separate encoding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate (Roche-Yeung-Hau 1997) and the entire admissible rate region (Yeung-Zhang 1999) of the general problem. This paper considers a natural generalization of SMDC to the secure communication setting with an additional eavesdropper. It is required that all sources need to be kept perfectly secret from the eavesdropper as long as the number of encoder outputs available at the eavesdropper is no more than a given threshold. First, the problem of encoding individual sources is studied. A precise characterization of the entire admissible rate region is established via a connection to the problem of ramp-type secret sharing (Yamamoto 1985 and Blakley-Meadows 1985) and utilizing some 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.

This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation of the problem is presented. A coding scheme that combines rate splitting, superposition coding, nested binning, and channel prefixing is considered and is shown to achieve the secrecy capacity region of the channel in several scenarios. Specifying these results to both scalar and independent parallel Gaussian channels (under an average individual per-subchannel power constraint), it is shown that the high-security message can be embedded into the low-security message at full rate (as if the low-security message does not exist) without incurring any loss on the overall rate of communication (as if both messages are low-security messages). Extensions to the wiretap channel II setting of Ozarow and Wyner are also considered, where it is shown that "perfect" security embedding can be achieved by an encoder that uses a two-level coset code.

This paper considers the problem of simultaneously communicating high-security and low-security messages, referred to as the security embedding problem. An information-theoretic model is presented. A coding scheme that combines superposition coding and random binning is proposed and is shown to achieve the capacity region in several communication scenarios. As an application, it is shown that a simple scheme that combines security embedding codes and secure network coding can achieve the secrecy capacity of a parallel multi-eavesdropper wiretap channel with two reversely degraded components.

This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the confidential message. The secrecy capacity region of the enhanced channel is characterized using an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel.