For DMC $(\mathcal{X},\mathcal{Y},Q=[P_{ij}])$ with information capacity $$C=\max_{p_{X}}I(X;Y)$$its operational capacity $C_{op}$ satisfies $$C_{op}=C$$ i.e. the following two results hold: 1. Forward Part (Achievability): For any $0<\epsilon<1$, there exists $\gamma=\gamma(\epsilon)>0$ and a sequence of $(n,M_{n})$ fixed-length codes $\mathcal{C}_{n}$ for the DMC with $$C>\liminf_{n\to\infty} \frac{1}{n}\log_{2}M_{n}\ge C-\gamma$$and $$P_{e}(\mathcal{C}_{n})<\epsilon$$for $n$ sufficiently large. 2. Converse Part: For any sequence of $(n,M_{n})$ fixed-length codes $\mathcal{C}_n$ for the DMC with $$\liminf_{n\to\infty} \frac{1}{n}\log_{2}M_{n}> C$$ we have that $$\lim_{n\to\infty}P_{e}(\mathcal{C}_{n})>0$$or that $P_{e}(\mathcal{C}_n)$ cannot asymptotically vanish (i.e. if our rate exceeds the channel capacity, we do not get low error of probability).