# Reconstruction of Correlated Sources with Energy Harvesting Constraints in Delay-constrained and Delay-tolerant Communication Scenarios

## TL;DR

This paper studies how to optimally reconstruct correlated sources in energy-harvesting sensor networks under delay constraints, proposing algorithms for power and rate allocation to minimize distortion.

## Contribution

It introduces a convex optimization framework and iterative algorithms for joint power and rate allocation in delay-constrained and delay-tolerant scenarios with energy harvesting.

## Key findings

- Optimal policies depend on delay constraints and source correlation.
- The proposed algorithms effectively minimize average distortion.
- Heuristic online policies show performance gaps compared to optimal solutions.

## 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.