607 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
Interference Alignment for the Multi-Antenna Compound Wiretap Channel
We study a wiretap channel model where the sender has transmit antennas
and there are two groups consisting of and receivers respectively.
Each receiver has a single antenna. We consider two scenarios. First we
consider the compound wiretap model -- group 1 constitutes the set of
legitimate receivers, all interested in a common message, whereas group 2 is
the set of eavesdroppers. We establish new lower and upper bounds on the secure
degrees of freedom. Our lower bound is based on the recently proposed
\emph{real interference alignment} scheme. The upper bound provides the first
known example which illustrates that the \emph{pairwise upper bound} used in
earlier works is not tight.
The second scenario we study is the compound private broadcast channel. Each
group is interested in a message that must be protected from the other group.
Upper and lower bounds on the degrees of freedom are developed by extending the
results on the compound wiretap channel.Comment: Minor edits. Submitted to IEEE Trans. Inf. Theor
Secrecy Capacity Region of Some Classes of Wiretap Broadcast Channels
This work investigates the secrecy capacity of the Wiretap Broadcast Channel
(WBC) with an external eavesdropper where a source wishes to communicate two
private messages over a Broadcast Channel (BC) while keeping them secret from
the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity
region of this channel which, in absence of security constraints, reduces to
the best known outer bound to the capacity of the standard BC. An inner bound
is also derived which follows the behavior of both the best known inner bound
for the BC and the Wiretap Channel. These bounds are shown to be tight for the
deterministic BC with a general eavesdropper, the semi-deterministic BC with a
more-noisy eavesdropper and the Wiretap BC where users exhibit a less-noisiness
order between them. Finally, by rewriting our outer bound to encompass the
characteristics of parallel channels, we also derive the secrecy capacity
region of the product of two inversely less-noisy BCs with a more-noisy
eavesdropper. We illustrate our results by studying the impact of security
constraints on the capacity of the WBC with binary erasure (BEC) and binary
symmetric (BSC) components.Comment: 19 pages, 8 figures, To appear in IEEE Trans. on Information Theor
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