12 research outputs found
On the Optimality of Treating Inter-Cell Interference as Noise in Uplink Cellular Networks
In this paper, we explore the information-theoretic optimality of treating
interference as noise (TIN) in cellular networks. We focus on uplink scenarios
modeled by the Gaussian interfering multiple access channel (IMAC), comprising
mutually interfering multiple access channels (MACs), each formed by an
arbitrary number of transmitters communicating independent messages to one
receiver. We define TIN for this setting as a scheme in which each MAC (or
cell) performs a power-controlled version of its capacity-achieving strategy,
with Gaussian codebooks and successive decoding, while treating interference
from all other MACs (i.e. inter-cell interference) as noise. We characterize
the generalized degrees-of-freedom (GDoF) region achieved through the proposed
TIN scheme, and then identify conditions under which this achievable region is
convex without the need for time-sharing. We then tighten these convexity
conditions and identify a regime in which the proposed TIN scheme achieves the
entire GDoF region of the IMAC and is within a constant gap of the entire
capacity region.Comment: Accepted for publication in IEEE Transactions on Information Theor
On the Optimality of Treating Interference as Noise: General Message Sets
In a K-user Gaussian interference channel, it has been shown that if for each
user the desired signal strength is no less than the sum of the strengths of
the strongest interference from this user and the strongest interference to
this user (all values in dB scale), then treating interference as noise (TIN)
is optimal from the perspective of generalized degrees-of-freedom (GDoF) and
achieves the entire channel capacity region to within a constant gap. In this
work, we show that for such TIN-optimal interference channels, even if the
message set is expanded to include an independent message from each transmitter
to each receiver, operating the new channel as the original interference
channel and treating interference as noise is still optimal for the sum
capacity up to a constant gap. Furthermore, we extend the result to the
sum-GDoF optimality of TIN in the general setting of X channels with arbitrary
numbers of transmitters and receivers
Cellular Networks With Finite Precision CSIT: GDoF Optimality of Multi-Cell TIN and Extremal Gains of Multi-Cell Cooperation
We study the generalized degrees-of-freedom (GDoF) of cellular networks under
finite precision channel state information at the transmitters (CSIT). We
consider downlink settings modeled by the interfering broadcast channel (IBC)
under no multi-cell cooperation, and the overloaded
multiple-input-single-output broadcast channel (MISO-BC) under full multi-cell
cooperation. We focus on three regimes of interest: the mc-TIN regime, where a
scheme based on treating inter-cell interference as noise (mc-TIN) was shown to
be GDoF optimal for the IBC; the mc-CTIN regime, where the GDoF region
achievable by mc-TIN is convex without the need for time-sharing; and the
mc-SLS regime which extends a previously identified regime, where a simple
layered superposition (SLS) scheme is optimal for the 3-transmitter-3-user
MISO-BC, to overloaded cellular-type networks with more users than
transmitters. We first show that the optimality of mc-TIN for the IBC extends
to the entire mc-CTIN regime when CSIT is limited to finite precision. The
converse proof of this result relies on a new application of aligned images
bounds. We then extend the IBC converse proof to the counterpart overloaded
MISO-BC, obtained by enabling full transmitter cooperation. This, in turn, is
utilized to show that a multi-cell variant of the SLS scheme is optimal in the
mc-SLS regime under full multi-cell cooperation, albeit only for 2-cell
networks. The overwhelming combinatorial complexity of the GDoF region stands
in the way of extending this result to larger networks. Alternatively, we
appeal to extremal network analysis, recently introduced by Chan et al., and
study the GDoF gain of multi-cell cooperation over mc-TIN in the three regimes
of interest. We show that this extremal GDoF gain is bounded by small constants
in the mc-TIN and mc-CTIN regimes, yet scales logarithmically with the number
of cells in the mc-SLS regime.Comment: Accepted for publication in the IEEE Transactions on Information
Theor
On Multi-Cell Uplink-Downlink Duality with Treating Inter-Cell Interference as Noise
We consider the information-theoretic optimality of treating inter-cell
interference as noise in downlink cellular networks modeled as Gaussian
interfering broadcast channels. Establishing a new uplink-downlink duality, we
cast the problem in Gaussian interfering broadcast channels to that in Gaussian
interfering multiple access channels, and characterize an achievable GDoF
region under power control and treating inter-cell interference as (Gaussian)
noise. We then identify conditions under which this achievable GDoF region is
optimal
Incremental Relaying for the Gaussian Interference Channel with a Degraded Broadcasting Relay
This paper studies incremental relay strategies for a two-user Gaussian
relay-interference channel with an in-band-reception and
out-of-band-transmission relay, where the link between the relay and the two
receivers is modelled as a degraded broadcast channel. It is shown that
generalized hash-and-forward (GHF) can achieve the capacity region of this
channel to within a constant number of bits in a certain weak relay regime,
where the transmitter-to-relay link gains are not unboundedly stronger than the
interference links between the transmitters and the receivers. The GHF relaying
strategy is ideally suited for the broadcasting relay because it can be
implemented in an incremental fashion, i.e., the relay message to one receiver
is a degraded version of the message to the other receiver. A
generalized-degree-of-freedom (GDoF) analysis in the high signal-to-noise ratio
(SNR) regime reveals that in the symmetric channel setting, each common relay
bit can improve the sum rate roughly by either one bit or two bits
asymptotically depending on the operating regime, and the rate gain can be
interpreted as coming solely from the improvement of the common message rates,
or alternatively in the very weak interference regime as solely coming from the
rate improvement of the private messages. Further, this paper studies an
asymmetric case in which the relay has only a single single link to one of the
destinations. It is shown that with only one relay-destination link, the
approximate capacity region can be established for a larger regime of channel
parameters. Further, from a GDoF point of view, the sum-capacity gain due to
the relay can now be thought as coming from either signal relaying only, or
interference forwarding only.Comment: To appear in IEEE Trans. on Inf. Theor
On the Optimality of Treating Inter-Cell Interference as Noise: Downlink Cellular Networks and Uplink-Downlink Duality
We consider the information-theoretic optimality of treating inter-cell
interference as noise (multi-cell TIN) in downlink cellular networks. We focus
on scenarios modeled by the Gaussian interfering broadcast channel (IBC),
comprising mutually interfering Gaussian broadcast channels (BCs), each
formed by a base station communicating independent messages to an arbitrary
number of users. We establish a new power allocation duality between the IBC
and its dual interfering multiple access channel (IMAC), which entails that the
corresponding generalized degrees-of-freedom regions achieved through
multi-cell TIN and power control (TINA regions) for both networks are
identical. As by-products of this duality, we obtain an explicit
characterization of the IBC TINA region from a previously established
characterization of the IMAC TINA region; and identify a multi-cell convex-TIN
regime in which the IBC TINA region is a polyhedron (hence convex) without the
need for time-sharing. We then identify a smaller multi-cell TIN regime in
which the IBC TINA region is optimal and multi-cell TIN achieves the entire
capacity region of the IBC, up to a constant gap. This is accomplished by
deriving a new genie-aided outer bound for the IBC, that reveals a novel
BC-type order that holds amongst users in each constituent BC (or cell) under
inter-cell interference, which in turn is not implied by previously known
BC-type orders (i.e. degraded, less noisy and more capable orders). The
multi-cell TIN regime that we identify for the IBC coincides with a
corresponding multi-cell TIN regime previously identified for the IMAC, hence
establishing a comprehensive uplink-downlink duality of multi-cell TIN in the
GDoF (and approximate capacity) sense
Multi-layer Interference Alignment and GDoF of the K-User Asymmetric Interference Channel
In wireless networks, link strengths are often affected by some topological
factors such as propagation path loss, shadowing and inter-cell interference.
Thus, different users in the network might experience different link strengths.
In this work we consider a K-user asymmetric interference channel, where the
channel gains of the links connected to Receiver k are scaled with P^{\alpha_k
/2}}, k=1,2,...,K, for 0< \alpha_1 \leq \alpha_2 \leq \cdots \leq \alpha_K \leq
1. For this setting, we show that the optimal sum generalized
degrees-of-freedom (GDoF) is characterized as dsum = (\sum_{k=1}^K \alpha_k +
\alpha_K -\alpha_{K-1})/2, which matches the existing result dsum= K/2 when
\alpha_1 = \alpha_2 = ... = \alpha_K =1. The achievability is based on
multi-layer interference alignment, where different interference alignment
sub-schemes are designed in different layers associated with specific power
levels, and successive decoding is applied at the receivers. While the converse
for the symmetric case only requires bounding the sum degrees-of-freedom (DoF)
for selected two users, the converse for this asymmetric case involves bounding
the weighted sum GDoF for selected J+2 users, with corresponding weights
(2^{J}, 2^{J-1}, ... , 2^{2}, 2^{1}), a geometric sequence with common ratio 2,
for the first J users and with corresponding weights (1, 1) for the last two
users, for J \in {1,2, ... , \lceil\log (K/2)\rceil }
Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?
Under the assumption of perfect channel state information at the transmitters
(CSIT), it is known that structured codes offer significant advantages for
secure communication in an interference network, e.g., structured jamming
signals based on lattice codes may allow a receiver to decode the sum of the
jamming signal and the signal being jammed, even though they cannot be
separately resolved due to secrecy constraints, subtract the aggregate jammed
signal, and then proceed to decode desired codewords at lower power levels. To
what extent are such benefits of structured codes fundamentally limited by
uncertainty in CSIT? To answer this question, we explore what is perhaps the
simplest setting where the question presents itself -- a Z interference channel
with secure communication. Using sum-set inequalities based on Aligned Images
bounds we prove that the GDoF benefits of structured codes are lost completely
under finite precision CSIT. The secure GDoF region of the Z interference
channel is obtained as a byproduct of the analysis.Comment: 34 pages, 10 figure
On the Gaussian Many-to-One X Channel
In this paper, the Gaussian many-to-one X channel, which is a special case of
general multiuser X channel, is studied. In the Gaussian many-to-one X channel,
communication links exist between all transmitters and one of the receivers,
along with a communication link between each transmitter and its corresponding
receiver. As per the X channel assumption, transmission of messages is allowed
on all the links of the channel. This communication model is different from the
corresponding many-to-one interference channel (IC). Transmission strategies
which involve using Gaussian codebooks and treating interference from a subset
of transmitters as noise are formulated for the above channel. Sum-rate is used
as the criterion of optimality for evaluating the strategies. Initially, a many-to-one X channel is considered and three transmission strategies
are analyzed. The first two strategies are shown to achieve sum-rate capacity
under certain channel conditions. For the third strategy, a sum-rate outer
bound is derived and the gap between the outer bound and the achieved rate is
characterized. These results are later extended to the case. Next,
a region in which the many-to-one X channel can be operated as a many-to-one IC
without loss of sum-rate is identified. Further, in the above region, it is
shown that using Gaussian codebooks and treating interference as noise achieves
a rate point that is within bits from the sum-rate capacity.
Subsequently, some implications of the above results to the Gaussian
many-to-one IC are discussed. Transmission strategies for the many-to-one IC
are formulated and channel conditions under which the strategies achieve
sum-rate capacity are obtained. A region where the sum-rate capacity can be
characterized to within bits is also identified.Comment: Submitted to IEEE Transactions on Information Theory; Revised and
updated version of the original draf