TY - GEN
T1 - Resolvability in Eγ with applications to lossy compression and wiretap channels
AU - Liu, Jingbo
AU - Cuff, Paul
AU - Verdu, Sergio
N1 - Funding Information:
This work was supported by NSF under Grants CCF- 1350595, CCF-1116013, CCF-1319299, CCF-1319304, and the Air Force Office of Scientific Research under Grant FA9550-12-1-0196
Publisher Copyright:
© 2015 IEEE.
PY - 2015/9/28
Y1 - 2015/9/28
N2 - We study the amount of randomness needed for an input process to approximate a given output distribution of a channel in the Eγ distance. A general one-shot achievability bound for the precision of such an approximation is developed. In the i.i.d. setting where γ = exp(nE), a (nonnegative) randomness rate above inf QU:D(Qxπx)≤ED(QXπX) + (QXU) - E is necessary and sufficient to asymptotically approximate the output distribution πXn using the channel QXn, where QU → QXU →QX. The new resolvability result is then used to derive a oneshot upper bound on the error probability in the rate distortion problem; and a lower bound on the size of the eavesdropper list to include the actual message in the wiretap channel problem. Both bounds are asymptotically tight in i.i.d. settings.
AB - We study the amount of randomness needed for an input process to approximate a given output distribution of a channel in the Eγ distance. A general one-shot achievability bound for the precision of such an approximation is developed. In the i.i.d. setting where γ = exp(nE), a (nonnegative) randomness rate above inf QU:D(Qxπx)≤ED(QXπX) + (QXU) - E is necessary and sufficient to asymptotically approximate the output distribution πXn using the channel QXn, where QU → QXU →QX. The new resolvability result is then used to derive a oneshot upper bound on the error probability in the rate distortion problem; and a lower bound on the size of the eavesdropper list to include the actual message in the wiretap channel problem. Both bounds are asymptotically tight in i.i.d. settings.
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U2 - 10.1109/ISIT.2015.7282556
DO - 10.1109/ISIT.2015.7282556
M3 - Conference contribution
AN - SCOPUS:84969799569
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 755
EP - 759
BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - IEEE International Symposium on Information Theory, ISIT 2015
Y2 - 14 June 2015 through 19 June 2015
ER -