5 research outputs found
Generalization of Mrs. Gerber's Lemma
Mrs. Gerber's Lemma (MGL) hinges on the convexity of , where
is the binary entropy function. In this work, we prove that
is convex in for every provided is convex in ,
where . Moreover, our result subsumes MGL and
simplifies the original proof. We show that the generalized MGL can be applied
in binary broadcast channel to simplify some discussion.Comment: Accepted by Communications in Information and System
On the inner and outer bounds of 3-receiver broadcast channels with 2-degraded message sets
We consider a broadcast channel with 3 receivers and 2 messages (M0, M1)
where two of the three receivers need to decode messages (M0, M1) while the
remaining one just needs to decode the message M0. We study the best known
inner and outer bounds under this setting, in an attempt to find the
deficiencies with the current techniques of establishing the bounds. We produce
a simple example where we are able to explicitly evaluate the inner bound and
show that it differs from the general outer bound. For a class of channels
where the general inner and outer bounds differ, we use a new argument to show
that the inner bound is tight.Comment: 5 pages
On The Capacity of Broadcast Channels With Degraded Message Sets and Message Cognition Under Different Secrecy Constraints
This paper considers a three-receiver broadcast channel with degraded message
sets and message cognition. The model consists of a common message for all
three receivers, a private common message for only two receivers and two
additional private messages for these two receivers, such that each receiver is
only interested in one message, while being fully cognizant of the other one.
First, this model is investigated without any secrecy constraints, where the
capacity region is established, showing that the straightforward extension of
the K\"orner and Marton inner bound to the investigated scenario is optimal. In
particular, this agrees with Nair and Wang's result, which states that the idea
of indirect decoding - introduced to improve the K\"orner and Marton inner
bound - does not provide a better region for this scenario. Further, some
secrecy constraints are introduced by letting the private messages to be
confidential ones. Two different secrecy criteria are considered: joint secrecy
and individual secrecy. For both criteria, a general achievable rate region is
provided. Moreover, the joint and individual secrecy capacity regions are
established, if the two legitimate receivers are more capable than the
eavesdropper. The established capacity regions indicate that the individual
secrecy criterion can provide a larger capacity region as compared to the joint
one, because each cognizant message can be used as a secret key for the other
individual message. Further, the joint secrecy capacity is established for a
more general class of more capable channels, where only one of the two
legitimate receivers is more capable than the eavesdropper. This was done by
showing that principle of indirect decoding introduced by Nair and El Gamal is
optimal for this class of channels. This result is in contrast with the
nonsecrecy case, where the indirect decoding does not provide any gain
Individual Secrecy for the Broadcast Channel
This paper studies the problem of secure communication over broadcast
channels under the individual secrecy constraints. That is, the transmitter
wants to send two independent messages to two legitimate receivers in the
presence of an eavesdropper, while keeping the eavesdropper ignorant of each
message (i.e., the information leakage from each message to the eavesdropper is
made vanishing). Building upon Carleial-Hellman's secrecy coding, Wyner's
secrecy coding, the frameworks of superposition coding and Marton's coding
together with techniques such as rate splitting and indirect decoding,
achievable rate regions are developed. The proposed regions are compared with
those satisfying joint secrecy and without secrecy constraints, and the
individual secrecy capacity regions for special cases are characterized. In
particular, capacity region for the deterministic case is established, and for
the Gaussian model, a constant gap (i.e., 0.5 bits within the individual
secrecy capacity region) result is obtained. Overall, when compared with the
joint secrecy constraint, the results allow for trading-off secrecy level and
throughput in the system.Comment: 49 pages, 13 figures, this paper was presented in part at IEEE
International Symposium on Information Theory, Hong Kong, Jun. 201
On 3-receiver broadcast channels with 2-degraded message sets
Abstract β We consider a broadcast channel with 3 receivers and 2 messages (M0, M1) where two of the three receivers need to decode messages (M0, M1) while the remaining one just needs to decode the message M0. We study the best known inner and outer bounds under this setting, in an attempt to find the deficiencies with the current techniques of establishing the bounds. We produce a simple example where we are able to explicitly evaluate the inner bound and show that it differs from the general outer bound. For a class of channels where the general inner and outer bounds differ, we use a new argument to show that the inner bound is tight. I