Title: Reconstruction of Correlated Sources with Energy Harvesting Constraints in Delay-constrained and Delay-tolerant Communication Scenarios,
Abstract: In this paper, we investigate the reconstruction of time-correlated sources
in a point-to-point communications scenario comprising an energy-harvesting
sensor and a Fusion Center (FC). Our goal is to minimize the average distortion
in the reconstructed observations by using data from previously encoded sources
as side information. First, we analyze a delay-constrained scenario, where the
sources must be reconstructed before the next time slot. We formulate the
problem in a convex optimization framework and derive the optimal transmission
(i.e., power and rate allocation) policy. To solve this problem, we propose an
iterative algorithm based on the subgradient method. Interestingly, the
solution to the problem consists of a coupling between a two-dimensional
directional water-filling algorithm (for power allocation) and a reverse
water-filling algorithm (for rate allocation). Then we find a more general
solution to this problem in a delay-tolerant scenario where the time horizon
for source reconstruction is extended to multiple time slots. Finally, we
provide some numerical results that illustrate the impact of delay and
correlation in the power and rate allocation policies, and in the resulting
reconstruction distortion. We also discuss the performance gap exhibited by a
heuristic online policy derived from the optimal (offline) one.