295 research outputs found
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
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
One-shot lossy quantum data compression
We provide a framework for one-shot quantum rate distortion coding, in which
the goal is to determine the minimum number of qubits required to compress
quantum information as a function of the probability that the distortion
incurred upon decompression exceeds some specified level. We obtain a one-shot
characterization of the minimum qubit compression size for an
entanglement-assisted quantum rate-distortion code in terms of the smooth
max-information, a quantity previously employed in the one-shot quantum reverse
Shannon theorem. Next, we show how this characterization converges to the known
expression for the entanglement-assisted quantum rate distortion function for
asymptotically many copies of a memoryless quantum information source. Finally,
we give a tight, finite blocklength characterization for the
entanglement-assisted minimum qubit compression size of a memoryless isotropic
qubit source subject to an average symbol-wise distortion constraint.Comment: 36 page
Oblivious data hiding : a practical approach
This dissertation presents an in-depth study of oblivious data hiding with the emphasis on quantization based schemes. Three main issues are specifically addressed:
1. Theoretical and practical aspects of embedder-detector design.
2. Performance evaluation, and analysis of performance vs. complexity tradeoffs.
3. Some application specific implementations.
A communications framework based on channel adaptive encoding and channel independent decoding is proposed and interpreted in terms of oblivious data hiding problem. The duality between the suggested encoding-decoding scheme and practical embedding-detection schemes are examined. With this perspective, a formal treatment of the processing employed in quantization based hiding methods is presented. In accordance with these results, the key aspects of embedder-detector design problem for practical methods are laid out, and various embedding-detection schemes are compared in terms of probability of error, normalized correlation, and hiding rate performance merits assuming AWGN attack scenarios and using mean squared error distortion measure.
The performance-complexity tradeoffs available for large and small embedding signal size (availability of high bandwidth and limitation of low bandwidth) cases are examined and some novel insights are offered. A new codeword generation scheme is proposed to enhance the performance of low-bandwidth applications. Embeddingdetection schemes are devised for watermarking application of data hiding, where robustness against the attacks is the main concern rather than the hiding rate or payload. In particular, cropping-resampling and lossy compression types of noninvertible attacks are considered in this dissertation work
Information Nonanticipative Rate Distortion Function and Its Applications
This paper investigates applications of nonanticipative Rate Distortion
Function (RDF) in a) zero-delay Joint Source-Channel Coding (JSCC) design based
on average and excess distortion probability, b) in bounding the Optimal
Performance Theoretically Attainable (OPTA) by noncausal and causal codes, and
computing the Rate Loss (RL) of zero-delay and causal codes with respect to
noncausal codes. These applications are described using two running examples,
the Binary Symmetric Markov Source with parameter p, (BSMS(p)) and the
multidimensional partially observed Gaussian-Markov source. For the
multidimensional Gaussian-Markov source with square error distortion, the
solution of the nonanticipative RDF is derived, its operational meaning using
JSCC design via a noisy coding theorem is shown by providing the optimal
encoding-decoding scheme over a vector Gaussian channel, and the RL of causal
and zero-delay codes with respect to noncausal codes is computed.
For the BSMS(p) with Hamming distortion, the solution of the nonanticipative
RDF is derived, the RL of causal codes with respect to noncausal codes is
computed, and an uncoded noisy coding theorem based on excess distortion
probability is shown. The information nonanticipative RDF is shown to be
equivalent to the nonanticipatory epsilon-entropy, which corresponds to the
classical RDF with an additional causality or nonanticipative condition imposed
on the optimal reproduction conditional distribution.Comment: 34 pages, 12 figures, part of this paper was accepted for publication
in IEEE International Symposium on Information Theory (ISIT), 2014 and in
book Coordination Control of Distributed Systems of series Lecture Notes in
Control and Information Sciences, 201
- …