Degraded broadcast channel: Secrecy outside of a bounded range

A three-receiver degraded broadcast channel with secrecy outside of a bounded range is studied, in which the channel quality gradually degrades from receiver 3 to receiver 1. The transmitter has three messages intended for the receivers with receiver 3 decoding all messages, receiver 2 decoding the first two messages, and receiver 1 decoding only the first message. Furthermore, the third message should be kept secure from receiver 1. The discrete memoryless channel is studied and the secrecy capacity region is characterized. The achievable scheme is based on superposition coding and random binning, in which one superposition layer and random binning together provide secrecy. The converse proof is derived based on the insight obtained from the achievable scheme so that manipulations of terms yield tight rate bounds.