An achievable rate region of a three-receiver BC with degraded message sets and side information

In this paper, a three-receiver (named as one-receiver two-eavesdropper) discrete memoryless broadcast channel (DM-BC) with three degraded message sets and side information is studied. The main objective of this paper is to present a theorem so as to give an achievable secrecy region for this one-receiver two-eavesdropper DM-BC with the side information available at the transmitter. In the achievability proof scheme, we use the superposition coding scheme to divide the available randomness into different levels for misleading the eavesdroppers. We establish the achievable secrecy region by using a combination of Gelfand-Pinsker binning scheme and rate splitting technique. Achievability in this case also follows from the new idea of Nair-El Gamal indirect decoding. The achievable secrecy region of this paper subsumes the steinberg rate region for two-receiver degraded BC with the side information as well as the secrecy capacity region for one-receiver two-eavesdropper DM-BC with no side information as its special cases.