Given integer $D\ge2, \ n\ge1$ and $K=K(n)$, a $(K,n)$ $D$-ary fixed-length (or block) code $\mathcal{C}$ for a DMS $\{X_i\}_{i=1}^\infty$ with alphabet $\mathcal{X}$ consists of all the following pair $(f,g)$ of encoding and decoding functions: ### Encoder: $$f:\mathcal{X}^n\to\{0,1,\cdots,D-1\}^K$$ ### Decoder: $$g:\{0,1,\cdots,D-1\}^K\to\mathcal{X}^n$$ The codebook is written as $$\mathcal{C}=f(\mathcal{X}^n)=\{f(a^n):a^n\in\mathcal{X}^n\}=\mbox{"set of codewords"}$$ where $f(a^n)$ is the codeword for source n-tuple $a^n$.