= Cyclic ternary channel capacity
{title2=$C=\log_2 3-h_2(q)$}
A <discrete memoryless channel> on the additive <group> $\mathbb Z/3\mathbb Z$ maps $x$ to $x$ with <probability> $1-q$ and to $x+1$ with <probability> $q$. Every input gives the same <conditional entropy> $h_2(q)$, whereas the output <Shannon entropy> is at most $\log_2 3$. A uniform input produces a uniform output since every column of the transition <matrix> sums to one. Hence the <channel capacity> is $\log_2 3-h_2(q)$ <bits> per use. This cyclic-error channel differs from a channel distributing its error probability equally over both other output symbols.
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