= Zero-rate distortion threshold
{title2=$D_{\mathrm{zero}}=\min_{\hat x}\mathbb E[d(X,\hat x)]$}
For the finite <alphabets> considered here, the <zero-rate distortion threshold> is the smallest <expected distortion> obtainable by always outputting one fixed reconstruction. Such a reconstruction is <independent> of the source, so its <mutual information> is zero. A randomized output that is <independent> of the source averages the costs of fixed reconstructions and cannot improve their minimum. Thus $R(D)=0$ exactly when $D\geq D_{\mathrm{zero}}$. For a fair <bit> under <Hamming distortion>, $D_{\mathrm{zero}}=1/2$; for a <Bernoulli random variable> of parameter $p$, it is $\min\{p,1-p\}$. The threshold depends on the source <probability distribution>, rather than only the <alphabet>.
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