On the rates-reliability-distortions and partial secrecy region of a one-stage branching communication system

A communication system is considered, where messages of K correlated sources X₁,...,X_K are encoded by a common encoder and two secondary encoders. At each receiver it is demanded: (i) to recover the messages of a part of the sources within given distortion levels, (ii) to keep secret the outputs of another part of the sources for receivers connected to the secondary encoders; and (iii) to disregard the information of the rest of the sources. It is required that for a given reliability E>0 at all receivers the error probabilities of the blocklength N code do not exceed 2^-NE. Inner and outer bounds on the region of achievable rates are established, depending on the reliability E and permissible distortion and secrecy levels