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Australian National University

1. Ding, Ni. Submodularity and Its Applications in Wireless Communications .

Degree: 2017, Australian National University

This monograph studies the submodularity in wireless communications and how to use it to enhance or improve the design of the optimization algorithms. The work is done in three different systems. In a cross-layer adaptive modulation problem, we prove the submodularity of the dynamic programming (DP), which contributes to the monotonicity of the optimal transmission policy. The monotonicity is utilized in a policy iteration algorithm to relieve the curse of dimensionality of DP. In addition, we show that the monotonic optimal policy can be determined by a multivariate minimization problem, which can be solved by a discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm. We show that the DSPSA is able to converge to the optimal policy in real time. For the adaptive modulation problem in a network-coded two-way relay channel, a two-player game model is proposed. We prove the supermodularity of this game, which ensures the existence of pure strategy Nash equilibria (PSNEs). We apply the Cournot tatonnement and show that it converges to the extremal, the largest and smallest, PSNEs within a finite number of iterations. We derive the sufficient conditions for the extremal PSNEs to be symmetric and monotonic in the channel signal-to-noise (SNR) ratio. Based on the submodularity of the entropy function, we study the communication for omniscience (CO) problem: how to let all users obtain all the information in a multiple random source via communications. In particular, we consider the minimum sum-rate problem: how to attain omniscience by the minimum total number of communications. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. We reveal the submodularity of the minimum sum-rate problem and propose polynomial time algorithms for solving it. We discuss the significance and applications of the fundamental partition, the one that gives rise to the minimum sum-rate in the asymptotic model. We also show how to achieve the omniscience in a successive manner.

Subjects/Keywords: submodularity; lattice; L-convexity; communication for omniscience; monotone comparative statics; Dilworth truncation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Ding, N. (2017). Submodularity and Its Applications in Wireless Communications . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/124067

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Ding, Ni. “Submodularity and Its Applications in Wireless Communications .” 2017. Thesis, Australian National University. Accessed September 25, 2020. http://hdl.handle.net/1885/124067.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Ding, Ni. “Submodularity and Its Applications in Wireless Communications .” 2017. Web. 25 Sep 2020.

Vancouver:

Ding N. Submodularity and Its Applications in Wireless Communications . [Internet] [Thesis]. Australian National University; 2017. [cited 2020 Sep 25]. Available from: http://hdl.handle.net/1885/124067.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ding N. Submodularity and Its Applications in Wireless Communications . [Thesis]. Australian National University; 2017. Available from: http://hdl.handle.net/1885/124067

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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