# The Gelfand-Pinsker Channel: Strong Converse and Upper Bound for the Reliability Function

## TL;DR

This paper establishes a strong converse for the capacity of the Gelfand-Pinsker channel and derives an upper bound on its reliability function, using a novel technical lemma related to codeword typicality.

## Contribution

It introduces a new technical lemma and proves a strong converse for the Gelfand-Pinsker channel capacity, advancing understanding of its reliability limits.

## Key findings

- Proved a strong converse for the Gelfand-Pinsker channel capacity.
- Derived an upper bound on the channel's reliability function.
- Developed a new technical lemma on codeword typicality.

## Abstract

We consider a Gelfand-Pinsker discrete memoryless channel (DMC) model and provide a strong converse for its capacity. The strong converse is then used to obtain an upper bound on the reliability function. Instrumental in our proofs is a new technical lemma which provides an upper bound for the rate of codes with codewords that are conditionally typical over large message dependent subsets of a typical set of state sequences. This technical result is a nonstraightforward analog of a known result for a DMC without states that provides an upper bound on the rate of a good code with codewords of a fixed type (to be found in, for instance, the Csiszar-Korner book).