[Show abstract][Hide abstract] ABSTRACT: We introduce the "blind index coding" (BIC) problem, which generalizes the
classic index coding problem by allowing the sender to have some uncertainty
about the side information that is available at each receiver. This problem
naturally arises in wireless networks, in which users obtain their side
information through wireless channels with errors that may be unknown to the
sender. For the proposed BIC problem, we develop a new general outer bound by
first proving it for the 3-user case, and then generalizing its construction to
K users. The proof of the outer bound relies on development of a key lemma that
uses a strong data processing inequality to account for the sender's
uncertainty. We also propose a hybrid coding scheme that XORs random
combinations of bits from a subset of messages with uncoded bits of other
messages in order to blindly exploit side information, and illustrate its gain.
We finally generalize the BIC problem to consider a wireless channel from
sender to users, and observe that even in the case of two users the solution
becomes non-trivial and a natural generalization of the hybrid coding scheme
relying on XORing repetitions of uncoded bits strictly outperforms conventional
schemes.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we study the communication problem from rovers on Mars'
surface to Mars-orbiting satellites. We first justify that, to a good extent,
the rover-to-orbiter communication problem can be modelled as communication
over a $2 \times 2$ X-channel with the network topology varying over time. For
such a fading X-channel where transmitters are only aware of the time-varying
topology but not the time-varying channel state (i.e., no CSIT), we establish
the sum degrees-of-freedom (DoF) by 1) proposing coding strategies that code
across topologies, and 2) developing novel upper bounds on the sum-DoF.
Furthermore we demonstrate that the proposed scheme approximately achieves the
ergodic sum capacity of the network. Using the proposed coding scheme, we
numerically evaluate the ergodic rate gain over a time-division-multiple-access
(TDMA) scheme for Rayleigh and Rice fading channels. We also numerically
demonstrate that with practical orbital parameters, a 9.6% DoF gain, as well as
more than 11.6% throughput gain can be achieved for a rover-to-orbiter
communication network.
[Show abstract][Hide abstract] ABSTRACT: Graph-based methods play an important role in unsupervised and
semi-supervised learning tasks by taking into account the underlying geometry
of the data set. In this paper, we consider a statistical setting for
semi-supervised learning and provide a formal justification of the recently
introduced framework of bandlimited interpolation of graph signals. Our
analysis leads to the interpretation that, given enough labeled data, this
method is very closely related to a constrained low density separation problem
as the number of data points tends to infinity. We demonstrate the practical
utility of our results through simple experiments.
[Show abstract][Hide abstract] ABSTRACT: We study the problem of interference management in fast fading wireless
networks, in which the transmitters are only aware of network topology. We
consider a class of retransmission-based schemes, where transmitters in the
network are only allowed to resend their symbols in order to assist with the
neutralization of interference at the receivers. We introduce a necessary and
sufficient condition on the network topology, under which half symmetric
degrees-of-freedom (DoF) is achievable through the considered
retransmission-based schemes. This corresponds to the "best" topologies since
half symmetric DoF is the highest possible value for the symmetric DoF in the
presence of interference. We show that when the condition is satisfied, there
always exists a set of carefully chosen transmitters in the network, such that
by retransmission of their symbols at an appropriate time slot, we can
neutralize all the interfering signals at the receivers. Quite surprisingly, we
also show that for any given network topology, if we cannot achieve half
symmetric DoF by retransmission-based schemes, then there does not exist any
linear scheme that can do so. We also consider a practical network scenario
that models cell edge users in a heterogeneous network, and show that the
characterized condition on the network topology occurs frequently. Furthermore,
we numerically evaluate the achievable rates of the DoF-optimal
retransmission-based scheme in such network scenario, and show that its
throughput gain is not restricted to the asymptotic DoF analysis.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of determining rank loss conditions for a
concatenation of full-rank matrices, such that each row of the composing
matrices is scaled by a random coefficient. This problem has applications in
wireless interference management and recommendation systems. We determine
necessary and sufficient conditions for the design of each matrix, such that
the random ensemble will almost surely lose rank by a certain amount. The
result is proved by converting the problem to determining rank loss conditions
for the union of some specific matroids, and then using tools from matroid and
graph theories to derive the necessary and sufficient conditions. As an
application, we discuss how this result can be applied to the problem of
topological interference management, and characterize the linear symmetric
degrees of freedom for a class of network topologies.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of sampling from data defined on the nodes of a
weighted graph, where the edge weights capture the data correlation structure.
As shown recently, using spectral graph theory one can define a cut-off
frequency for the bandlimited graph signals that can be reconstructed from a
given set of samples (i.e., graph nodes). In this work, we show how this
cut-off frequency can be computed exactly. Using this characterization, we
provide efficient algorithms for finding the subset of nodes of a given size
with the largest cut-off frequency and for finding the smallest subset of nodes
with a given cut-off frequency. In addition, we study the performance of random
uniform sampling when compared to the centralized optimal sampling provided by
the proposed algorithms.
[Show abstract][Hide abstract] ABSTRACT: Computing optimal half-duplex schedules in Gaussian relay networks is a challenging problem due to the lack of an exact capacity characterization and the large number of transmit-receive configurations that must be considered. We approach the problem using a constant-gap capacity approximation based on the cut-set bound with independent encoding at the nodes. We formulate an optimization problem to obtain the cut-set optimal half-duplex schedule and find that it is hard to solve in general. This is because it involves an exponential number of variables, since the number of ways to assign each node to either transmitter or receiver mode is exponential in the number of nodes. We present a general technique that takes advantage of specific structures in the topology of a given network and allows us to reduce the complexity of this problem. In certain classes of network topologies, our approach yields polynomial time algorithms for finding half-duplex schedules that achieve capacity within a constant gap. We use simulations to show running time improvements over alternative methods and compare the performance of various half-duplex scheduling approaches in different SNR regimes.
IEEE Transactions on Information Theory 11/2014; 60(11):7204-7220. DOI:10.1109/TIT.2014.2359440 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of broadcast over wireless erasure networks. To understand the challenges and opportunities of these setups, we study a two-hop erasure broadcast channel consisting of a single source, two relays, and two destinations desiring independent messages. In our network, no transmitter has channel state knowledge of erasures on outgoing links (i.e., no CSIT): The source has no knowledge of any channel state, each relay only has knowledge of the channel states of its incoming link, and destinations are provided with full channel knowledge. We propose a scheme, referred to as Align-and-Forward, that exploits the (unknown) common subspace of received signals at the relays, which results from the source-to-relay broadcast, in order to minimize the dimension of the interference subspace at each destination. We show that Align-and-Forward outperforms available alternative schemes in terms of sum-rate. We also present new outer-bounds and demonstrate the optimality of Align-and-Forward in certain regimes.
2014 IEEE International Symposium on Information Theory (ISIT); 06/2014
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of the two-user multiple-input single-output complex
Gaussian Broadcast Channel where the transmitter has access to delayed
knowledge of the channel state information. We characterize the capacity region
of this channel to within a constant number of bits for all values of the
transmit power. The proposed signaling strategy utilizes the delayed knowledge
of the channel state information and the previously transmitted signals, in
order to create a signal of common interest for both receivers. This signal is
the quantized version of the summation of the previously transmitted signals.
To guarantee the independence of quantization noise and signal, we extend the
framework of lattice quantizers with dither, together with an interleaving
step. For converse, we use the fact that the capacity region of this problem is
upper-bounded by the capacity region of a physically degraded broadcast channel
with no channel state information where one receiver has two antennas. We then
derive an outer-bound on the capacity region of this degraded broadcast channel
which in turn provides an outer-bound on the capacity region of the two-user
multiple-input single-output complex Gaussian broadcast channel with delayed
knowledge of the channel state information. By careful examination, we show
that the achievable rate region and the outer-bound are within 1.81 bits/sec/Hz
per user.
[Show abstract][Hide abstract] ABSTRACT: We study the degrees of freedom (DoF) of the multiple-input multiple-output
X-channel (MIMO XC) with delayed channel state information at the transmitters
(delayed CSIT), assuming linear coding strategies at the transmitters. We
present two results: 1) the linear sum DoF for MIMO XC with general antenna
configurations, and 2) the linear DoF region for MIMO XC with symmetric
antennas. The converse for each result is based on developing a novel
rank-ratio inequality that characterizes the maximum ratio between the
dimensions of received linear subspaces at the two multiple-antenna receivers.
The achievability of the linear sum DoF is based on a three-phase strategy, in
which during the first two phases only the transmitter with fewer antennas
exploits delayed CSIT in order to minimize the dimension of its signal at the
unintended receiver. During Phase 3, both transmitters use delayed CSIT to send
linear combinations of past transmissions such that each receiver receives a
superposition of desired message data and known interference, thus
simultaneously serving both receivers. We also derive other linear DoF outer
bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF
converse and the proposed transmission strategy, allow us to characterize the
linear DoF region for symmetric antenna configurations.
[Show abstract][Hide abstract] ABSTRACT: We consider the Gaussian wiretap channel where a transmitter wishes to
communicate a secure message to a legitimate receiver in the presence of
eavesdroppers, without the eavesdroppers being able to decode the secure
message. We focus on a setting that the transmitter is blind with respect to
the state of channels to eavesdroppers, and only has access to delayed channel
state information (CSI) of the legitimate receiver, which is referred to as
"blind wiretap channel with delayed CSIT". We then consider two scenarios: (i)
the case where the secure communication is aided via a distributed jammer, (ii)
the case where all nodes in the network are equipped with multiple antennas,
referred to as blind MIMO wiretap channel with delayed CSIT. We completely
characterize the secure Degrees of Freedom (SDoF) in both scenarios, when
assuming linear coding strategies at the transmitter(s).
[Show abstract][Hide abstract] ABSTRACT: We characterize the capacity region of the two-user Binary Fading
Interference Channel where the transmitters have no knowledge of the channel
state information. We show that the entire capacity region is achieved by
applying point-to-point erasure codes with appropriate rates at each
transmitter, and using either treat-interference-as-erasure or
interference-decoding at each receiver, based on the channel parameters. The
result is obtained by developing a novel outer-bound that has three main steps.
We first create a contracted channel that has fewer states compared to the
original channel, in order to make the analysis tractable. Using a Correlation
Lemma, we then show that an outer-bound on the capacity region of the
contracted channel also serves as an outer-bound for the original channel.
Finally, using a Conditional Entropy Leakage Lemma, we derive our outer-bound
on the capacity region of the contracted channel, and show that it coincides
with the achievable region by either treat-interference-as-erasure or
interference-decoding at each receiver. We also show that having access to
delayed local knowledge of the channel state information, does not enlarge the
capacity region.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of the two-user multiple-input single-output complex Gaussian Broadcast Channel where the transmitter has access to delayed knowledge of the channel state information. We characterize the capacity region of this channel to within a constant number of bits for all values of the transmit power. The proposed signaling strategy utilizes the delayed knowledge of the channel state information and the previously transmitted signals, in order to create a signal of common interest for both receivers. This signal is the quantized version of the summation of the previously transmitted signals. To guarantee the independence of quantization noise and signal, we extend the framework of lattice quantizers with dither, together with an interleaving step. For converse, we use the fact that the capacity region of this problem is upper-bounded by the capacity region of a physically degraded broadcast channel with no channel state information where one receiver has two antennas. We then derive an outer-bound on the capacity region of this degraded broadcast channel which in turn provides an outer-bound on the capacity region of the two-user multiple-input single-output complex Gaussian broadcast channel with delayed knowledge of the channel state information. By careful examination, we show that the achievable rate region and the outer-bound are within 1.81 bits/sec/Hz per user.
[Show abstract][Hide abstract] ABSTRACT: We study the degrees of freedom (DoF) of the multiple-input multiple-output X-channel (MIMO XC) with delayed channel state information at the transmitters (delayed CSIT), assuming linear coding strategies at the transmitters. We present two results: 1) the linear sum DoF for MIMO XC with general antenna configurations, and 2) the linear DoF region for MIMO XC with symmetric antennas. The converse for each result is based on developing a novel rank-ratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multiple-antenna receivers. The achievability of the linear sum DoF is based on a three-phase strategy, in which during the first two phases only the transmitter with fewer antennas exploits delayed CSIT in order to minimize the dimension of its signal at the unintended receiver. During Phase 3, both transmitters use delayed CSIT to send linear combinations of past transmissions such that each receiver receives a superposition of desired message data and known interference, thus simultaneously serving both receivers. We also derive other linear DoF outer bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF converse and the proposed transmission strategy, allow us to characterize the linear DoF region for symmetric antenna configurations.
[Show abstract][Hide abstract] ABSTRACT: We present a new outer bound for the sum capacity of general multi-unicast
deterministic networks. Intuitively, this bound can be understood as applying
the cut-set bound to concatenated copies of the original network with a special
restriction on the allowed transmit signal distributions. We first study
applications to finite-field networks, where we obtain a general outer-bound
expression in terms of ranks of the transfer matrices. We then show that, even
though our outer bound is for deterministic networks, a recent result relating
the capacity of AWGN KxKxK networks and the capacity of a deterministic
counterpart allows us to establish an outer bound to the DoF of KxKxK wireless
networks with general connectivity. This bound is tight in the case of the
"adjacent-cell interference" topology, and yields graph-theoretic necessary and
sufficient conditions for K DoF to be achievable in general topologies.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of spectrum sharing in wireless communication networks composed of multiple source-destination pairs. We define a novel concept of information-theoretic independent sets (in short, ITIS) which indicates the sets of source-destination pairs in the network inside each of which, treating interference as noise is information-theoretically optimal (to within a constant gap). Then, we propose a new spectrum sharing scheme called information-theoretic link scheduling (in short, ITLinQ), which at each time schedules those users that form an ITIS. We first provide a performance guarantee of the ITLinQ scheme through characterizing the fraction of the capacity region that it can achieve in a network with source and destination nodes spread randomly in a fixed area. Moreover, we will show how to implement the ITLinQ scheme in a distributed fashion by using an initial 2-phase signaling mechanism which provides the required channel state information at all the nodes. Finally, we compare the performance of the distributed ITLinQ scheme with similar state-of-the-art spectrum sharing mechanisms, such as FlashLinQ, through numerical analysis and show that it can exhibit a sum-rate gain of more than a 100%, while keeping the complexity at the same level.
2014 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN); 04/2014
[Show abstract][Hide abstract] ABSTRACT: The layered interference network is investigated with delayed channel state information (CSI) at all nodes. It is demonstrated how multihopping can be utilized to increase the achievable degrees of freedom (DoF). In particular, a multiphase transmission scheme is proposed for the $K$-user $2K$-hop interference network to systematically exploit the layered structure of the network and delayed CSI to achieve DoF values that scale with $K$. This result provides the first example of a network with distributed transmitters and delayed CSI whose DoF scales with the number of users.
IEEE Transactions on Information Theory 03/2014; 60(3):1822-1839. DOI:10.1109/TIT.2013.2290539 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: When several wireless users are sharing the spectrum, packet collision is a
simple, yet widely used model for interference. Under this model, when
transmitters cause interference at any of the receivers, their collided packets
are discarded and need to be retransmitted. However, in reality, that receiver
can still store its analog received signal and utilize it for decoding the
packets in the future (for example, by successive interference cancellation
techniques). In this work, we propose a physical layer model for wireless
packet networks that allows for such flexibility at the receivers. We assume
that the transmitters will be aware of the state of the channel (i.e. when and
where collisions occur, or an unintended receiver overhears the signal) with
some delay, and propose several coding opportunities that can be utilized by
the transmitters to exploit the available signal at the receivers for
interference management (as opposed to discarding them). We analyze the
achievable throughput of our strategy in a canonical interference channel with
two transmitter-receiver pairs, and demonstrate the gain over conventional
schemes. By deriving an outer-bound, we also prove the optimality of our scheme
for the corresponding model.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of spectrum sharing in device-to-device communication
systems. Inspired by the recent optimality condition for treating interference
as noise, we define a new concept of "information-theoretic independent sets"
(ITIS), which indicates the sets of users for which simultaneous communication
and treating the interference from each other as noise is
information-theoretically optimal (to within a constant gap). Based on this
concept, we develop a new spectrum sharing mechanism, called
"information-theoretic link scheduling" (ITLinQ), which at each time schedules
those users that form an ITIS. We first provide a performance guarantee for
ITLinQ by characterizing the fraction of the capacity region that it can
achieve in a network with sources and destinations located randomly within a
fixed area. Furthermore, we demonstrate how ITLinQ can be implemented in a
distributed manner, using an initial 2-phase signaling mechanism which provides
the required channel state information at all the users. Finally, through
numerical analysis, we show that distributed ITLinQ can outperform similar
state-of-the-art spectrum sharing mechanisms, such as FlashLinQ, by more than a
%100 of sum-rate gain, while keeping the complexity at the same level.
IEEE Journal on Selected Areas in Communications 11/2013; 32(6). DOI:10.1109/JSAC.2014.2328102 · 3.45 Impact Factor