復号手法
P ( x received ∣ y sent ) = P ( x received , y sent ) P ( y sent ) = P ( y sent ∣ x received ) ⋅ P ( x received ) P ( y sent ) ∝ P ( y sent ∣ x received ) {\displaystyle {\begin{aligned}\mathbb {P} (x{\mbox{ received}}\mid y{\mbox{ sent}})&{}={\frac {\mathbb {P} (x{\mbox{ received}},y{\mbox{ sent}})}{\mathbb {P} (y{\mbox{ sent}})}}\\&{}=\mathbb {P} (y{\mbox{ sent}}\mid x{\mbox{ received}})\cdot {\frac {\mathbb {P} (x{\mbox{ received}})}{\mathbb {P} (y{\mbox{ sent}})}}\\&{}\propto \mathbb {P} (y{\mbox{ sent}}\mid x{\mbox{ received}})\end{aligned}}}
最終行では x received {\displaystyle x{\mbox{ received}}} が固定されていることと、 P ( y sent ) {\displaystyle \mathbb {P} (y{\mbox{ sent}})} が y sent {\displaystyle y{\mbox{ sent}}} 依存性を持たないことを使っている。なお「最適復号」と同様、確率が同じ符号語がある場合の規定をしておく必要がある。