The conventional channel resolvability refers to the minimum rate needed for an input process to approximate the channel output distribution in total variation distance. In this paper, we study E_γ-resolvability, in which total variation is replaced by the more general E_γ distance. A general one-shot achievability bound for the precision of such an approximation is developed. Let Q_X|U be a random transformation, n be an integer, and E ∈ (0, +∞). We show that in the asymptotic setting where γ = exp(nE), a (nonnegative) randomness rate above inf Q_U:D_{(QXIIπX)≤E}{D(Q_XIIπ_X) + I(Q_U, Q_X|U) - E} is sufficient to approximate the output distribution π_X^⊗n using the channel Q_X|U^⊗n, where Q_U → Q_X|U → Q_X, and is also necessary in the case of finite U and X . In particular, a randomness rate of inf Q_U I(Q_U, Q_X|U) - E is always sufficient. We also study the convergence of the approximation error under the high-probability criteria in the case of random codebooks. Moreover, by developing simple bounds relating E_γ and other distance measures, we are able to determine the exact linear growth rate of the approximation errors measured in relative entropy and smooth Rényi divergences for a fixed-input randomness rate. The new resolvability result is then used to derive: 1) a one-shot upper bound on the probability of excess distortion in lossy compression, which is exponentially tight in the i.i.d. setting; 2) a one-shot version of the mutual covering lemma; and 3) a l- wer bound on the size of the eavesdropper list to include the actual message and a lower bound on the eavesdropper false-alarm probability in the wiretap channel problem, which is (asymptotically) ensemble-tight.

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integer relative entropy oneshot achievability bounds fixedinput randomness esubx03b3sub distance linear growth rate lossy compression upper bound total variation channel qsubxusubsupx2297nsup output distribution x03c0subxsubsupx2297nsup esubx03b3subresolvability e x2208 usub e oneshot version of the mutual covering lemma qsubusub x2192 qsubxusub x2192 qsubxsub smooth rex0301nyi divergences probability of excess distortion wer approximation errors random codebooks highprobability criteria eavesdropper falsealarm probability inf qsubusub iusub

Jingbo Liu,.$E_{ {gamma }}$ -Resolvability. 63 (5),2629-2658.

Jingbo Liu,"$E_{ {gamma }}$ -Resolvability" 63

Jingbo Liu,"$E_{ {gamma }}$ -Resolvability"