Manuscript Em05-B@1 · Em05-B-v1.tex · corollary · 6c050f5b

Corollary: Certified recovery enclosure

Referenced certification interfaces › Model error, decoder error, and diagnostic stability · lines 1966–1992 · proof included or linked

Em05-B@1#cor:enclosure

A channel certificate $ξ$ , together with (eq:improvedSandwich), yields

max {0, B (η) - ξ} \leq ε_{rec} (N) \leq min {1, min {t, \frac{3}{4}, U (η)} + ξ} .

If an implemented decoder satisfies $d_{⋄} (D, D) \leq ζ$ , then

d_{⋄} (D N, id_{M}) \leq min {1, d_{⋄} (D N_{η}, id_{M}) + ξ + ζ} .

Proof. Apply Proposition prop:stability. For the implemented decoder, telescope the composition and use pre- and postprocessing contraction.

Displayed formulas in this passage

unlabeled · line 1970
$max {0, B (η) - ξ} \leq ε_{rec} (N) \leq min {1, min {t, \frac{3}{4}, U (η)} + ξ} .$
unlabeled · line 1981
$d_{⋄} (D N, id_{M}) \leq min {1, d_{⋄} (D N_{η}, id_{M}) + ξ + ζ} .$