Complete-access restoration is a decoder with a larger input

The map $\mathcal{L}:RB\to C$ is a complete-access quantum decoder. It is not generally a radiation-only decoder $R\to C$. It is also not a unitary inverse on every state of $RB$: the second term is an off-code completion. On the specified encoded range, complete coherent access allows reversal of the preparation and evolution.

This corrects the possible shorthand “the restore map is not a decoder.” Its mathematical task is decoding; the issue is which input interface it requires.