Let $(X,\mathcal A,\mu,T)$ be an invertible measure-preserving system, where $T:X\to X$ is measurable, has a measurable inverse, and satisfies $\mu(T^{-1}E)=\mu(E)$ for every $E\in\mathcal A$. Let $\mathcal P=\{P_a:a\in A\}$ be a countable generating partition indexed by $A$. Let $\mathcal B$ be the product $\sigma$-algebra on $A^{\mathbb Z}$. Then the coding map $\pi_{\mathcal P}:X\to A^{\mathbb Z}$ defines a factor map from $(X,\mathcal A,\mu,T)$ to the shift system $(A^{\mathbb Z},\mathcal B,(\pi_{\mathcal P})_*\mu,S)$. Moreover, the induced map identifies the measure algebra of $(X,\mathcal A,\mu)$ with the measure algebra of the coded image modulo $(\pi_{\mathcal P})_*\mu$-null sets.