Manuscript Hawk05-B@1 · Hawk05-B.tex · section · f2e5d4f5

A smaller code: a conservative complete-channel certificate

The Page curve and whole-code recovery are different tasks › A smaller code: a conservative complete-channel certificate · lines 1095–1120

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This theorem supplies a channel estimate not inferred from the Page entropy slope. It deliberately retains the input-dimension factor in the Choi-to-diamond conversion.

An early-access comparison follows by interchanging $r$ and $b$ :

γ_{R} = \frac{( 1 - d ^{- 2} ) b ( r ^{2} - 1 )}{D ^{2} - 1}, Λ_{R} = \frac{d}{2} d r γ_{R} .

With probability at least $1 - α$ ,

d_{⋄} (N, T_{N (I_{C} / d)}) \leq min {1, Λ_{R} / α},

and therefore

ε_{rec} (N) \geq max {0, a_{d} - Λ_{R} / α} .

Early replacement and late recovery are thus separate proved comparisons in the Haar subcode model.

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unlabeled · line 1102
$γ_{R} = \frac{( 1 - d ^{- 2} ) b ( r ^{2} - 1 )}{D ^{2} - 1}, Λ_{R} = \frac{d}{2} d r γ_{R} .$
unlabeled · line 1110
$d_{⋄} (N, T_{N (I_{C} / d)}) \leq min {1, Λ_{R} / α},$
unlabeled · line 1115
$ε_{rec} (N) \geq max {0, a_{d} - Λ_{R} / α} .$

A smaller code: a conservative complete-channel certificate

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