Manuscript Em03-E@1 · Em03-E-v1.tex · proposition · c4b07e6a

Proposition: Decoded channel

E4: explicit decoder and optimal referenced recovery › A complete decoder · lines 821–837 · proof included or linked

Em03-E@1#prop:decoded, Em03-E@1#eq:decoded

The exact decoded channel is

D N_{2} = p Λ_{η} + (1 - p) T .

Proof. In each successful key block the correction removes $P_{ab}$ , while the failure block is replaced by $I_{2} /2$ . The key weights sum to one, and the count densities have trace one. This proves the identity on all message operators.

Displayed formulas in this passage

Em03-E@1#eq:decoded · line 824
$D N_{2} = p Λ_{η} + (1 - p) T .$

Nearby in this section

section: A complete decoder