# Compressing the output of a discrete memoryless channel

Let $$x\in \mathcal{X}$$ be a symbol from an input alphabet, let $$p(y|x)$$ be a conditional probability distribution corresponding to a discrete memoryless channel and let $$y\in\mathcal{Y}$$ be an output alphabet. Given that the channel has capacity $$C$$, is it true that one can compress any $$n-$$bit output to $$nC$$ bits with error in the compression vanishing as $$n\rightarrow\infty$$?

The motivation for this comes from the reverse Shannon theorem established in Section IV of https://arxiv.org/pdf/quant-ph/0106052.pdf. To simulate a channel, Alice applies the channel locally and then transfers the output to Bob. She does this in a clever way such that only $$2^{nC}$$ bits of communication is actually required.

I was wondering if her protocol is equivalent to compressing the channel output and sending it over to Bob.