2,256 research outputs found
Inner and Outer Bounds for the Gaussian Cognitive Interference Channel and New Capacity Results
The capacity of the Gaussian cognitive interference channel, a variation of
the classical two-user interference channel where one of the transmitters
(referred to as cognitive) has knowledge of both messages, is known in several
parameter regimes but remains unknown in general. In this paper we provide a
comparative overview of this channel model as we proceed through our
contributions: we present a new outer bound based on the idea of a broadcast
channel with degraded message sets, and another series of outer bounds obtained
by transforming the cognitive channel into channels with known capacity. We
specialize the largest known inner bound derived for the discrete memoryless
channel to the Gaussian noise channel and present several simplified schemes
evaluated for Gaussian inputs in closed form which we use to prove a number of
results. These include a new set of capacity results for the a) "primary
decodes cognitive" regime, a subset of the "strong interference" regime that is
not included in the "very strong interference" regime for which capacity was
known, and for the b) "S-channel" in which the primary transmitter does not
interfere with the cognitive receiver. Next, for a general Gaussian cognitive
interference channel, we determine the capacity to within one bit/s/Hz and to
within a factor two regardless of channel parameters, thus establishing rate
performance guarantees at high and low SNR, respectively. We also show how
different simplified transmission schemes achieve a constant gap between inner
and outer bound for specific channels. Finally, we numerically evaluate and
compare the various simplified achievable rate regions and outer bounds in
parameter regimes where capacity is unknown, leading to further insight on the
capacity region of the Gaussian cognitive interference channel.Comment: submitted to IEEE transaction of Information Theor
Approximate Sum-Capacity of K-user Cognitive Interference Channels with Cumulative Message Sharing
This paper considers the K user cognitive interference channel with one
primary and K-1 secondary/cognitive transmitters with a cumulative message
sharing structure, i.e cognitive transmitter knows non-causally
all messages of the users with index less than i. We propose a computable outer
bound valid for any memoryless channel. We first evaluate the sum-rate outer
bound for the high- SNR linear deterministic approximation of the Gaussian
noise channel. This is shown to be capacity for the 3-user channel with
arbitrary channel gains and the sum-capacity for the symmetric K-user channel.
Interestingly. for the K user channel having only the K th cognitive know all
the other messages is sufficient to achieve capacity i.e cognition at
transmitter 2 to K-1 is not needed. Next the sum capacity of the symmetric
Gaussian noise channel is characterized to within a constant additive and
multiplicative gap. The proposed achievable scheme for the additive gap is
based on Dirty paper coding and can be thought of as a MIMO-broadcast scheme
where only one encoding order is possible due to the message sharing structure.
As opposed to other multiuser interference channel models, a single scheme
suffices for both the weak and strong interference regimes. With this scheme
the generalized degrees of freedom (gDOF) is shown to be a function of K, in
contrast to the non cognitive case and the broadcast channel case.
Interestingly, it is show that as the number of users grows to infinity the
gDoF of the K-user cognitive interference channel with cumulative message
sharing tends to the gDoF of a broadcast channel with a K-antenna transmitter
and K single-antenna receivers. The analytical additive additive and
multiplicative gaps are a function of the number of users. Numerical
evaluations of inner and outer bounds show that the actual gap is less than the
analytical one.Comment: Journa
A New Capacity Result for the Z-Gaussian Cognitive Interference Channel
This work proposes a novel outer bound for the Gaussian cognitive
interference channel in strong interference at the primary receiver based on
the capacity of a multi-antenna broadcast channel with degraded message set. It
then shows that for the Z-channel, i.e., when the secondary receiver
experiences no interference and the primary receiver experiences strong
interference, the proposed outer bound not only is the tightest among known
bounds but is actually achievable for sufficiently strong interference. The
latter is a novel capacity result that from numerical evaluations appears to be
generalizable to a larger (i.e., non-Z) class of Gaussian channels
On Discrete Alphabets for the Two-user Gaussian Interference Channel with One Receiver Lacking Knowledge of the Interfering Codebook
In multi-user information theory it is often assumed that every node in the
network possesses all codebooks used in the network. This assumption is however
impractical in distributed ad-hoc and cognitive networks. This work considers
the two- user Gaussian Interference Channel with one Oblivious Receiver
(G-IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook while
the other receiver knows both codebooks. We ask whether, and if so how much,
the channel capacity of the G-IC- OR is reduced compared to that of the
classical G-IC where both receivers know all codebooks. Intuitively, the
oblivious receiver should not be able to jointly decode its intended message
along with the unintended interfering message whose codebook is unavailable. We
demonstrate that in strong and very strong interference, where joint decoding
is capacity achieving for the classical G-IC, lack of codebook knowledge does
not reduce performance in terms of generalized degrees of freedom (gDoF).
Moreover, we show that the sum-capacity of the symmetric G-IC- OR is to within
O(log(log(SNR))) of that of the classical G-IC. The key novelty of the proposed
achievable scheme is the use of a discrete input alphabet for the non-oblivious
transmitter, whose cardinality is appropriately chosen as a function of SNR
- β¦