On the closeness of distribution of some random variable to the equiprobable one

Let $b \geqslant 2$ and $N$ be natural numbers, $X_0,X_1,\ldots ,X_{n-1}$ be nonhomogeneous sequence of independent random variables taking values $0, 1,\ldots , b-1$,
$$Y_{n}=X_{0}+bX_{1}+\ldots+X_{n-2}b^{n-2}+X_{n-1}b^{n-1}$$
and
$$Z_{n}=Y_{n}\text{ mod }N.$$
We estimate the closeness of distribution of random variable $Z_n$ to the uniform distribution on $\{0,1,\ldots,N-1\}$ in the case when $b$ and $N$ are mutually prime.