In multi-terminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs a joint unique de
coding of messages of interest along with a subset of messages which are not of interest. It is now well-known that this provides an achievable region which is, in general, larger than if the receiver treats all messages not of interest as noise. Nair and El Gamal (2009) and Chong, Motani, Garg, and El Gamal (2008) independently proposed a generalization called indirect or non-unique decoding where the receiver uses the codebook structure of the messages to uniquely decode only its messages of interest. Non-unique decoding has since been used in various scenarios. The main result in this paper is to provide an interpretation and a systematic proof technique for why non-unique decoding, in all known cases where it has been employed, can be replaced by a particularly designed joint unique decoding strategy, without any penalty from a rate region viewpoint.
Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are a
vailable -- correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution and prove its optimality for the parallel channels and sources case when each sub-channel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper). This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated.
