1 research outputs found
Submodularity and Its Applications in Wireless Communications
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