# Lower Bound of Rate-Reliability-Distortion Function for Generalized Channel With Side Information

## Abstract

In this paper we study a generalized model of discrete memoryless channel (DMC) with finite 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. Reasoning 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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