Since there are $k={k}_{1}+\cdots +{k}_{M}$ message bits, the rate of the overall multilevel code is given as $R=k/n={\sum}_{i=1}^{M}{k}_{i}/n$. The minimum distance of the overall multilevel code is derived as

${d}_{\text{min,}\mathcal{C}}={\displaystyle \underset{i\in \{1\text{,}\dots \text{,}M\}}{\mathrm{min}}}{d}_{i}{\delta}_{i}^{2}\text{.}$ (12)

(12)

As an example, consider a multilevel code of block length $n=8$: the first level component code is the repetition code with ${k}_{1}=8\text{,}{d}_{1}$

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