# Random Coding Bound for Secrecy E-capacity Region of the Broadcast Channel With Two Confidential Messages

## Keywords:

Broadcast channel with confidential messages, secrecy E-capacity, equivocation rate, error probability exponent, method of types, random coding bound## Abstract

We study secrecy E-capacity region of the discrete memoryless broadcast channel with two independent confidential messages sent to two receivers (BC-2CM). The system involves two sources, one encoder, two discrete memoryless channels and two receivers. Each private message is sent to the corresponding receiver while keeping the other receiver in total ignorance of it. The level of ignorance is measured by the equivocation rate. E-capacity region is the set of rate pairs R1; R2 of codes with given error probability exponents (reliabilities) E1; E2 at respective receivers. We derived a random coding bound for secrecy E-capacity region of the BC-2CM. When error probability exponents are going to zero, this bound coincides with the inner bound of secrecy capacity region of the BC-2CM obtained by R. Liu, I. Maric, P. Spasojevic and R. Yates.

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*Mathematical Problems of Computer Science*,

*36*, 79–90. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/269

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