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Mathematical Problems of Computer Science 33, 11{23, 2010.

Lower B ound of Rate-Reliability-Distor tion Function

for Gener alized Channel With Side I nfor mation

Ma r ia m E . H a r o u t u n ia n a n d A r t h u r R . Mu r a d ya n

Institute for Informatics and Automation Problems of NAS of RA

e-mail: armar@ipia.sci.am

Abstract

In this paper we study a generalized model of discrete memoryless channel (DMC)

with ¯nite input and output alphabets and random state sequence (side information)

partially known to the encoder, channel and decoder. The study includes the family of

Gel'fand-Pinsker and information hiding coding problems as special cases. Information

is to be reliably transmitted through the noisy channel selected by adversary. Reason-

ing from applications the actions of encoder and adversary are limited by distortion

constraints. The encoder and decoder depend on a random variable (RV) which can be

treated as cryptographic key. Two cases are considered, when the joint distribution of

this RV and side information is given or this RV is independent from side information

and it's distribution can be chosen for the best code generation. We investigate the

rate-reliability-distortion function for the mentioned model and derive the lower bound

for it.

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