7,733 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
The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents
We consider the secret key generation problem when sources are randomly
excited by the sender and there is a noiseless public discussion channel. Our
setting is thus similar to recent works on channels with action-dependent
states where the channel state may be influenced by some of the parties
involved. We derive single-letter expressions for the secret key capacity
through a type of source emulation analysis. We also derive lower bounds on the
achievable reliability and secrecy exponents, i.e., the exponential rates of
decay of the probability of decoding error and of the information leakage.
These exponents allow us to determine a set of strongly-achievable secret key
rates. For degraded eavesdroppers the maximum strongly-achievable rate equals
the secret key capacity; our exponents can also be specialized to previously
known results.
In deriving our strong achievability results we introduce a coding scheme
that combines wiretap coding (to excite the channel) and key extraction (to
distill keys from residual randomness). The secret key capacity is naturally
seen to be a combination of both source- and channel-type randomness. Through
examples we illustrate a fundamental interplay between the portion of the
secret key rate due to each type of randomness. We also illustrate inherent
tradeoffs between the achievable reliability and secrecy exponents. Our new
scheme also naturally accommodates rate limits on the public discussion. We
show that under rate constraints we are able to achieve larger rates than those
that can be attained through a pure source emulation strategy.Comment: 18 pages, 8 figures; Submitted to the IEEE Transactions on
Information Theory; Revised in Oct 201
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor
Bounds on Information Combining With Quantum Side Information
"Bounds on information combining" are entropic inequalities that determine
how the information (entropy) of a set of random variables can change when
these are combined in certain prescribed ways. Such bounds play an important
role in classical information theory, particularly in coding and Shannon
theory; entropy power inequalities are special instances of them. The arguably
most elementary kind of information combining is the addition of two binary
random variables (a CNOT gate), and the resulting quantities play an important
role in Belief propagation and Polar coding. We investigate this problem in the
setting where quantum side information is available, which has been recognized
as a hard setting for entropy power inequalities.
Our main technical result is a non-trivial, and close to optimal, lower bound
on the combined entropy, which can be seen as an almost optimal "quantum Mrs.
Gerber's Lemma". Our proof uses three main ingredients: (1) a new bound on the
concavity of von Neumann entropy, which is tight in the regime of low pairwise
state fidelities; (2) the quantitative improvement of strong subadditivity due
to Fawzi-Renner, in which we manage to handle the minimization over recovery
maps; (3) recent duality results on classical-quantum-channels due to Renes et
al. We furthermore present conjectures on the optimal lower and upper bounds
under quantum side information, supported by interesting analytical
observations and strong numerical evidence.
We finally apply our bounds to Polar coding for binary-input
classical-quantum channels, and show the following three results: (A) Even
non-stationary channels polarize under the polar transform. (B) The blocklength
required to approach the symmetric capacity scales at most sub-exponentially in
the gap to capacity. (C) Under the aforementioned lower bound conjecture, a
blocklength polynomial in the gap suffices.Comment: 23 pages, 6 figures; v2: small correction
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