15 research outputs found
Informational Divergence Approximations to Product Distributions
The minimum rate needed to accurately approximate a product distribution
based on an unnormalized informational divergence is shown to be a mutual
information. This result subsumes results of Wyner on common information and
Han-Verd\'{u} on resolvability. The result also extends to cases where the
source distribution is unknown but the entropy is known
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
On Channel Resolvability in Presence of Feedback
We study the problem of generating an approximately i.i.d. string at the
output of a discrete memoryless channel using a limited amount of randomness at
its input in presence of causal noiseless feedback. Feedback does not decrease
the channel resolution, the minimum entropy rate required to achieve an
accurate approximation of an i.i.d. output string. However, we show that, at
least over a binary symmetric channel, a significantly larger resolvability
exponent (the exponential decay rate of the divergence between the output
distribution and product measure), compared to the best known achievable
resolvability exponent in a system without feedback, is possible. We show that
by employing a variable-length resolvability scheme and using an average number
of coin-flips per channel use, the average divergence between the distribution
of the output sequence and product measure decays exponentially fast in the
average length of output sequence with an exponent equal to
where is the mutual information developed across the channel.Comment: 8 pages, 4 figures; to be presented at the 54th Annual Allerton
Conference on Communication, Control, and Computin
Exact Random Coding Secrecy Exponents for the Wiretap Channel
We analyze the exact exponential decay rate of the expected amount of
information leaked to the wiretapper in Wyner's wiretap channel setting using
wiretap channel codes constructed from both i.i.d. and constant-composition
random codes. Our analysis for those sampled from i.i.d. random coding ensemble
shows that the previously-known achievable secrecy exponent using this ensemble
is indeed the exact exponent for an average code in the ensemble. Furthermore,
our analysis on wiretap channel codes constructed from the ensemble of
constant-composition random codes leads to an exponent which, in addition to
being the exact exponent for an average code, is larger than the achievable
secrecy exponent that has been established so far in the literature for this
ensemble (which in turn was known to be smaller than that achievable by wiretap
channel codes sampled from i.i.d. random coding ensemble). We show examples
where the exact secrecy exponent for the wiretap channel codes constructed from
random constant-composition codes is larger than that of those constructed from
i.i.d. random codes and examples where the exact secrecy exponent for the
wiretap channel codes constructed from i.i.d. random codes is larger than that
of those constructed from constant-composition random codes. We, hence,
conclude that, unlike the error correction problem, there is no general
ordering between the two random coding ensembles in terms of their secrecy
exponent.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
Wiretap and Gelfand-Pinsker Channels Analogy and its Applications
An analogy framework between wiretap channels (WTCs) and state-dependent
point-to-point channels with non-causal encoder channel state information
(referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of
stealth-wiretap codes is shown to induce a good sequence of codes for a
corresponding GPC. Consequently, the framework enables exploiting existing
results for GPCs to produce converse proofs for their wiretap analogs. The
analogy readily extends to multiuser broadcasting scenarios, encompassing
broadcast channels (BCs) with deterministic components, degradation ordering
between users, and BCs with cooperative receivers. Given a wiretap BC (WTBC)
with two receivers and one eavesdropper, an analogous Gelfand-Pinsker BC (GPBC)
is constructed by converting the eavesdropper's observation sequence into a
state sequence with an appropriate product distribution (induced by the
stealth-wiretap code for the WTBC), and non-causally revealing the states to
the encoder. The transition matrix of the state-dependent GPBC is extracted
from WTBC's transition law, with the eavesdropper's output playing the role of
the channel state. Past capacity results for the semi-deterministic (SD) GPBC
and the physically-degraded (PD) GPBC with an informed receiver are leveraged
to furnish analogy-based converse proofs for the analogous WTBC setups. This
characterizes the secrecy-capacity regions of the SD-WTBC and the PD-WTBC, in
which the stronger receiver also observes the eavesdropper's channel output.
These derivations exemplify how the wiretap-GP analogy enables translating
results on one problem into advances in the study of the other