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Markov Approximation for Combinatorial Network Optimization
"... Many important network design problems can be formulated as a combinatorial optimization problem. A large number of such problems, however, cannot readily be tackled by distributed algorithms. The Markov approximation framework studied in this paper is a general technique for synthesizing distribut ..."
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Cited by 31 (14 self)
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Many important network design problems can be formulated as a combinatorial optimization problem. A large number of such problems, however, cannot readily be tackled by distributed algorithms. The Markov approximation framework studied in this paper is a general technique for synthesizing distributed algorithms. We show that when using the log-sum-exp function to approximate the optimal value of any combinatorial problem, we end up with a solution that can be interpreted as the stationary probability distribution of a class of timereversible Markov chains. Certain carefully designed Markov chains among this class yield distributed algorithms that solve the log-sum-exp approximated combinatorial network optimization problem. By three case studies, we illustrate that Markov approximation technique not only can provide fresh perspective to existing distributed solutions, but also can help us generate new distributed algorithms in various domains with provable performance. We believe the Markov approximation techniques will find application in many network optimization problems, and this paper serves as a call for participation of it.
On the optimality of treating interference as noise
- in Proc. 51st Annu. Allerton Conf. Commun., Control, Comput
, 2013
"... Abstract — It is shown that in the K-user interference channel, 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 decibel scale), then the simple scheme of usin ..."
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Cited by 9 (4 self)
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Abstract — It is shown that in the K-user interference channel, 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 decibel scale), then the simple scheme of using point-to-point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise (TIN) at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron, which is shown to be fully achieved by the same scheme, without the need for time-sharing. The results are proved by first deriving a polyhedral relaxation of the GDoF region achieved by TIN, and then providing a dual characterization of this polyhedral region via the use of potential functions, and finally proving the optimality of this region in the desired regime. Index Terms — Capacity region, Gaussian interference channel, generalized degrees of freedom (GDoF), treating interference as noise (TIN). I.
On the maximum achievable sum-rate with successive decoding in interference channels
- IEEE Trans. Inf. Theory
, 2012
"... Abstract—In this paper, we investigate the maximum achievable sum-rate of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that ..."
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Cited by 4 (1 self)
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Abstract—In this paper, we investigate the maximum achievable sum-rate of the two-user Gaussian interference channel with Gaussian superposition 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 find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theo-retic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum
On the sum-capacity with successive decoding in interference channels. submitted to
- IEEE Transactions on Information Theory
"... Abstract—In this paper, we investigate the sum-capacity of the two-user 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 u ..."
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Cited by 2 (1 self)
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Abstract—In this paper, we investigate the sum-capacity of the two-user 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 sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity 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 sum-rate 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 sum-capacity. Numerical evaluations show that the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Gaussian Han-Kobayashi schemes and that with single message schemes. I.
TCP Reno over Adaptive CSMA
, 2010
"... Any person(s) intending to use a part or the whole of the materials in this thesis in a proposed publication must seek copyright release from the Dean of ..."
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Any person(s) intending to use a part or the whole of the materials in this thesis in a proposed publication must seek copyright release from the Dean of
