D:\sbornik\...\tpel.DVI


Mathematical Problems of Computer Science 36, 79{90, 2012.

Random Coding B ound for Secr ecy E-capacity Region

of the B r oadcast Channel With T wo Con¯dential

M essages

N a s r in A fs h a r , E vg u e n i H a r o u t u n ia n a n d Ma r ia m H a r o u t u n ia n

Institute for Informatics and Automation Problems of NAS of RA

e-mail: evhar@ipia.sci.am

Abstract

We study secrecy E-capacity region of the discrete memoryless broadcast chan-
nel with two independent con¯dential 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.

Key words: Broadcast channel with con¯dential messages, secrecy E-capacity,
equivocation rate, error probability exponent, method of types, random coding bound.

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