= Hamming distortion
{title2=$d(x,\hat x)=\mathbf1_{\{x\ne\hat x\}}$}
<Hamming distortion> is zero for a correctly reconstructed symbol and one for a mismatch. Its <expected distortion> is the symbol-error <probability>:
$$
\mathbb E[d(X,\widehat X)]=\mathbb P(X\ne\widehat X).
$$
For strings of length $n$, <separable distortion> divides their <Hamming distance> by $n$. Thus $001$ reconstructed as $000$ has <Hamming distance> one and average <Hamming distortion> $1/3$. Counting only whether the whole string is correct would give a different criterion.
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