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Keywords
(8)
Capacity Region
Channel Model
Gaussian Channel
Interference Channel
Oscillations
Power Allocation
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On the SumCapacity with Successive Decoding in Interference Channels
On the SumCapacity with Successive Decoding in Interference Channels,10.1109/ISIT.2011.6033790,Yue Zhao,Chee Wei Tan,Amir Salman Avestimehr,Suhas N.
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On the SumCapacity with Successive Decoding in Interference Channels
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Citations: 1
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Yue Zhao
,
Chee Wei Tan
,
Amir Salman Avestimehr
,
Suhas N. Diggavi
,
Gregory J. Pottie
In this paper, we investigate the sumcapacity of the twouser Gaussian
interference channel
with Gaussian su perposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we show that the constrained sumcapacity oscillates as a function of the cross link gain parameters between the
information theoretic
sumcapacity and the sumcapacity with interference treated as noise. Furthermore, we show that if the number of messages of either user is fewer than the minimum number required to achieve the constrained sum capacity, the maximum achievable sumrate drops to that with interference treated as noise. We translate the optimal schemes in the deterministic
channel model
to the
Gaussian channel
model, and also derive two upper bounds on the constrained sumcapacity. Numerical evaluations show that the constrained sumcapacity in the Gaussian channels oscillates between the sumcapacity with Gaussian HanKobayashi schemes and that with single message schemes. I. INTRODUCTION We consider the sumrate maximization problem in two user Gaussian interference channels under the constraints of successive decoding. While the
information theoretic
capacity region
of the Gaussian
interference channel
is still not known, it has been shown that a HanKobayashi scheme with random Gaussian codewords can achieve within 1 bit/s/Hz of the ca pacity region (4). In this scheme, each user decodes both users' common messages jointly, and then decodes its own private message. In comparison, the simplest decoding constraint is treating the interference from the other users as noise. It has been shown that within a certain range of channel parameters for weak interference channels, treating interference as noise achieves the
information theoretic
sumcapacity (1), (6), (7). In this paper, we consider a decoding constraint — succes sive decoding of Gaussian superposition codewords —t hat bridges the complexity between joint decoding (e.g. in Han Kobayashi schemes) and treating interference as noise. We investigate the constrained sumcapacity and how to achieve it. To clarify and capture the key aspects of the problem, we resort to a deterministic
channel model
(2). In (3), the
information theoretic
capacity region
for the twouser deterministic inter ference channel is derived as a special case of the El Gamal Costa deterministic model (5), and is shown to be achievable using HanKobayashi schemes. To capture the use of successive decoding of Gaussian codewords, we introduce the complementarity conditions on the bit levels in the deterministic formulation. We develop transmission schemes on the bitlevels, which in the Gaussian model corresponds to message splitting and
power allocation
of the messages. We then solve the constrained sumcapacity, and show that it oscillates (as a function of the cross link gain parameters) between the
information theoretic
sumcapacity and the sumcapacity with interference treated as noise. Fur thermore, the minimum number of messages needed to achieve the constrained sumcapacity is obtained. We show that if the number of messages is limited to even one less than this minimum capacity achieving number, the sumcapacity drops to that with interference treated as noise. We then translate the optimal scheme in the deterministic
interference channel
to the Gaussian channel, using a rate constraint equalization technique. To evaluate the optimality of the translated achievable schemes, we derive two upper bounds on the sumcapacity with Gaussian HanKobayashi schemes, which automatically apply to the sumcapacity with successive decoding schemes. The two bounds are shown to be tight in different ranges of parameters. The remainder of the paper is organized as follows. Section II formulates the problem of sumcapacity with successive decoding of Gaussian codewords in Gaussian interference channels. Section III reformulates the problem with the de terministic channel model, and then solves the constrained sumcapacity. Section IV translates the optimal schemes in the deterministic channel back to the Gaussian channel, and derives two upper bounds on the constrained sumcapacity. Conclusions are drawn in Section V. Due to space limitations, all the proofs are omitted here, and can be found in (9). II. PROBLEM FORMULATION IN GAUSSIAN CHANNELS
Conference:
IEEE International Symposium on Information Theory  ISIT
, vol. abs/1103.0, pp. 14941498, 2011
DOI:
10.1109/ISIT.2011.6033790
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Citation Context
(1)
...Conclusions are drawn in Section V. Due to space limitations, all the proofs are omitted here, and can be found in [
9
]...
...Complete solutions in asymmetric channels follow similar ideas. The details can be found in [
9
]...
...We propose the following power allocation algorithm that equalizes the rate constraints, in which L counts the number of messages used by each user. The derivations can be found in [
9
]...
...More specifically, the bounds are derived for the sumcapacity with Gaussian HanKobayashi schemes, which automatically upper bound the sumcapacity with successive decoding of Gaussian codewords, (as Gaussian superposition coding  successive decoding is a special case of HanKobayashi schemes [
9
])...
...It is worth noting that although the above differences (1.8 bits and 1.0 bits) with SNR =3 0dB may not seem very significant, as SNR →∞ , both differences will go to infinity [
9
]...
Yue Zhao
,
et al.
On the SumCapacity with Successive Decoding in Interference Channels
References
(9)
Gaussian interference networks: sum capacity in the lowinterference regime and new outer bounds on the capacity region
(
Citations: 51
)
V. Sreekanth Annapureddy
,
Venugopal V. Veeravalli
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 55, no. 7, pp. 30323050, 2009
Wireless Network Information Flow: A Deterministic Approach
(
Citations: 15
)
Amir Salman Avestimehr
,
Suhas N. Diggavi
,
David N. C. Tse
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 57, no. 4, pp. 18721905, 2011
The twouser Gaussian interference channel: a deterministic view
(
Citations: 65
)
Guy Bresler
,
David Tse
Journal:
Computing Research Repository  CORR
, vol. abs/0807.3, no. 4, pp. 333354, 2008
Gaussian Interference Channel Capacity to Within One Bit
(
Citations: 265
)
Raul H. Etkin
,
David N. C. Tse
,
Hua Wang
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 54, no. 12, pp. 55345562, 2008
The capacity region of a class of deterministic interference channels
(
Citations: 101
)
Abbas A. El Gamal
,
Max H. M. Costa
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 28, no. 2, 1982
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Citations
(1)
On the SumCapacity with Successive Decoding in Interference Channels
(
Citations: 1
)
Yue Zhao
,
Chee Wei Tan
,
Amir Salman Avestimehr
,
Suhas N. Diggavi
,
Gregory J. Pottie
Conference:
IEEE International Symposium on Information Theory  ISIT
, vol. abs/1103.0, pp. 14941498, 2011