Direct radiation observation and observation after recovery

Directly measuring $R$ denotes a channel

not a quantum decoder.

For observation after recovery, let $F$ be a specified basis-selection unitary on the encoded output and append

Cout := F(Cout); x := Enter(Cout); returnBit(x);

The observable channel is ${\mathcal{M}}_F\mathcal{D}{\mathcal{N}}_t$. Its intended target is ${\mathcal{M}}_F$, not ${\mathrm{id}}_C$. For non-power-of-two codes, ${\mathcal{M}}_F$ includes the declared padded implementation and logical restriction.