Given positive integers $n$ and $M$, an $(n,M)$ fixed-length code for a discrete channel $(\mathcal{X},\mathcal{Y}, \{P_{Y^{n}|X^{n}}\}_{n=1}^{\infty})$ with code length $n$ and rate $R_{n}:=\frac{1}{n}\log_{2}M$ message bits/channel use consists of: - a message set $\mathcal{M}=\{1,\cdots,M\}$ intended for transmission - an encoding function $$f:\mathcal{M}\to\mathcal{X}^{n}$$yielding codewords $f(1),\cdots,f(M)\in\mathcal{X}^{n}$ of length $n$. The set of codewords is called the codebook, written as $$\mathcal{C}_{n}=\{f(1),\cdots,f(M)\}$$ - a decoding function $$g:\mathcal{Y}^{n}\to\mathcal{M}$$