54 research outputs found
Strong Converse and Second-Order Asymptotics of Channel Resolvability
We study the problem of channel resolvability for fixed i.i.d. input
distributions and discrete memoryless channels (DMCs), and derive the strong
converse theorem for any DMCs that are not necessarily full rank. We also
derive the optimal second-order rate under a condition. Furthermore, under the
condition that a DMC has the unique capacity achieving input distribution, we
derive the optimal second-order rate of channel resolvability for the worst
input distribution.Comment: 7 pages, a shorter version will appear in ISIT 2014, this version
includes the proofs of technical lemmas in appendice
Resolvability on Continuous Alphabets
We characterize the resolvability region for a large class of point-to-point
channels with continuous alphabets. In our direct result, we prove not only the
existence of good resolvability codebooks, but adapt an approach based on the
Chernoff-Hoeffding bound to the continuous case showing that the probability of
drawing an unsuitable codebook is doubly exponentially small. For the converse
part, we show that our previous elementary result carries over to the
continuous case easily under some mild continuity assumption.Comment: v2: Corrected inaccuracies in proof of direct part. Statement of
Theorem 3 slightly adapted; other results unchanged v3: Extended version of
camera ready version submitted to ISIT 201
MAC Resolvability: First And Second Order Results
Building upon previous work on the relation between secrecy and channel
resolvability, we revisit a secrecy proof for the multiple-access channel from
the perspective of resolvability. We then refine the approach in order to
obtain some novel results on the second-order achievable rates.Comment: Slightly extended version of the paper accepted at the 4th Workshop
on Physical-Layer Methods for Wireless Security during IEEE CNS 2017. v2:
Fixed typos and extended literature section in accordance with reviewers'
recommendation
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects
Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels
We propose a quantum soft-covering problem for a given general quantum
channel and one of its output states, which consists in finding the minimum
rank of an input state needed to approximate the given channel output. We then
prove a one-shot quantum covering lemma in terms of smooth min-entropies by
leveraging decoupling techniques from quantum Shannon theory. This covering
result is shown to be equivalent to a coding theorem for rate distortion under
a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan,
arXiv:2302.00625]. Both one-shot results directly yield corollaries about the
i.i.d. asymptotics, in terms of the coherent information of the channel.
The power of our quantum covering lemma is demonstrated by two additional
applications: first, we formulate a quantum channel resolvability problem, and
provide one-shot as well as asymptotic upper and lower bounds. Secondly, we
provide new upper bounds on the unrestricted and simultaneous identification
capacities of quantum channels, in particular separating for the first time the
simultaneous identification capacity from the unrestricted one, proving a
long-standing conjecture of the last author.Comment: 29 pages, 3 figures; v2 fixes an error in Definition 6.1 and various
typos and minor issues throughou
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