On the Optimality of Treating Interference as Noise: General Message Sets

Sun, Hua Yan; Jafar, Syed A.

doi:10.48550/arxiv.1401.2592

Cited by 3 publications

(6 citation statements)

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“…Remark 2: A similar result is proved for the K × K XC in [18], where they show that under certain channel conditions, strategy M1, i.e., treating interference as noise at the receivers is sum generalized degrees-of-freedom (GDoF) optimal and also achieves a constant gap to the sum-rate capacity. This result can be specialized to the many-to-one XC, and after some manipulations, the channel conditions in [18,Theorem 2] essentially boil down to sub-region (39), where it is shown that the gap from the sum-rate capacity is within K 2 log 2 K(K + 1) bits. Note that the gap from the sum-rate capacity is larger than that in Theorem 6, owing to the fact that the bounding techniques as well as the results in [18] are applicable to the general fully connected K × K XC.…”

Section: Bmentioning

confidence: 55%

“…This result can be specialized to the many-to-one XC, and after some manipulations, the channel conditions in [18,Theorem 2] essentially boil down to sub-region (39), where it is shown that the gap from the sum-rate capacity is within K 2 log 2 K(K + 1) bits. Note that the gap from the sum-rate capacity is larger than that in Theorem 6, owing to the fact that the bounding techniques as well as the results in [18] are applicable to the general fully connected K × K XC.…”

Section: Bmentioning

confidence: 95%

“…XC in [17], [18] to show that under the same channel conditions, treating interference as noise is optimal in terms of sum-rate capacity up to a constant gap. In [19], a constant gap capacity approximation for the 2 × 2 XC subject to an outage set has been obtained.…”

Section: M3mentioning

confidence: 99%

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On the Gaussian Many-to-One X Channel

Prasad

Bhashyam

Chockalingam

2016

IEEE Trans. Inform. Theory

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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 $3 \times 3$ 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 $K \times K$ 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 $K/2 -1$ 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 $K/2-1$ bits is also identified.Comment: Submitted to IEEE Transactions on Information Theory; Revised and updated version of the original draf

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Section: Bmentioning

confidence: 55%

Section: Bmentioning

confidence: 95%

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On the Gaussian Many-to-One X Channel

Prasad

Bhashyam

Chockalingam

2016

IEEE Trans. Inform. Theory

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“…Note that for general compound interference channels, P φ (i.e., the polyhedral TIN region for the case in which all the users are active) is the same as the polyhedral TIN region P defined in Section 2.1, i.e., P = P φ . When ( 20) is satisfied, the polyhedral TIN region P φ subsumes all the others and P * = P. Remark 3 It is also not hard to extend the result of Theorem 1 to the sum-GDoF optimality of TIN for M ×N compound X channels following [36]. In addition, based on the bounding techniques provided in [10,36], it is easy to prove that under the same condition (20), power control and TIN is sufficient to achieve a constant gap to the capacity region of the K-user compound interference channel, and the constant gap result can also be generalized to compound X channels in terms of the sum capacity.…”

Section: Potential Graphmentioning

confidence: 99%

“…6(c), where there are 4 messages totally. According to Remark 3, following [36], we know that even if the message set is increased, the sum-GDoF of this compound X channel remains as 1, which is apparently achievable by setting W 12 = W 21 = φ, sending only {W 11 , W 22 } through the channel with appropriate power levels and treating interference as noise at each receiver.…”

Section: Potential Graphmentioning

confidence: 99%

On the Optimality of Treating Interference as Noise: Compound Interference Networks

Geng

Jafar

2016

IEEE Trans. Inform. Theory

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In a K-user Gaussian interference channel, it has been shown by Geng et al. 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 power control and 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 generalize the optimality of TIN to compound networks. We show that for a K-user compound Gaussian interference channel, if in every possible state for each receiver, the channel always satisfies the TIN-optimality condition identified by Geng et al., then the GDoF region of the compound channel is the intersection of the GDoF regions of all possible network realizations, which is achievable by power control and TIN. Furthermore, we demonstrate that for a general K-user compound interference channel, regardless of the number of states of each receiver, we can always construct a counterpart K-user regular interference channel that has the same TIN region as the original compound channel. The regular interference channel has only one state for each receiver, which may be different from all of the original states. Solving the GDoF-based power control problem for the compound channel is equivalent to solving the same problem in its regular counterpart. Exploring the power control problem further we develop a centralized power control scheme for K-user compound interference channels, to achieve all the Pareto optimal GDoF tuples. Finally, based on this scheme, we devise an iterative power control algorithm which requires at most K updates to obtain the globally optimal power allocation for any feasible GDoF tuple.

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Extended generalized DoF optimality regime of treating interference as noise in the X channel

Gherekhloo

Chaaban

Sezgin

2014

2014 11th International Symposium on Wireless Communications Systems (ISWCS)

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Abstract-The simple scheme of treating interference as noise (TIN) is studied in this paper for the 3 × 2 X channel. A new sum-capacity upper bound is derived. This upper bound is transformed into a generalized degrees-of-freedom (GDoF) upper bound, and is shown to coincide with the achievable GDoF of a scheme that combines TDMA and TIN for some conditions on the channel parameters. These conditions specify a noisy interference regime which extends noisy interference regimes available in literature. As a by-product, the sum-capacity of the 3 × 2 X channel is characterized within a constant gap in the given noisy interference regime.

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On the Optimality of Treating Interference as Noise: General Message Sets

Cited by 3 publications

References 0 publications

On the Gaussian Many-to-One X Channel

On the Gaussian Many-to-One X Channel

On the Optimality of Treating Interference as Noise: Compound Interference Networks

Extended generalized DoF optimality regime of treating interference as noise in the X channel

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