Capacity of the Binary Energy Harvesting Channel

2025-02-11

AI Summary

This paper addresses the capacity of binary energy-harvesting (EH) channels with finite batteries, focusing on the noiseless binary EH channel (BEHC), whose capacity lacks a computable closed-form expression. Method: We propose a novel causal state-aware finite-state channel modeling framework, coupled with a tailored Q-graph construction (with controllable node count $N$), which exactly characterizes the channel capacity as a solvable convex optimization problem. Contribution/Results: Our method yields computable and convergent upper and lower bounds, enabling the first numerical capacity evaluation with $10^{-6}$-level precision for the BEHC. It extends to the binary symmetric EH channel with feedback. We compute high-precision capacities for battery efficiency $eta in {0.1,dots,0.9}$, significantly tightening existing bounds; additionally, we provide achievable rates for the feedback setting. This work establishes the first rigorous, high-accuracy, and scalable theoretical framework for capacity analysis of EH communication systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The capacity of a channel with an energy-harvesting (EH) encoder and a finite battery remains an open problem, even in the noiseless case. A key instance of this scenario is the binary EH channel (BEHC), where the encoder has a unit-sized battery and binary inputs. Existing capacity expressions for the BEHC are not computable, motivating this work, which determines the capacity to any desired precision via convex optimization. By modeling the system as a finite-state channel with state information known causally at the encoder, we derive single-letter lower and upper bounds using auxiliary directed graphs, termed $Q$-graphs. These $Q$-graphs exhibit a special structure with a finite number of nodes, $N$, enabling the formulation of the bounds as convex optimization problems. As $N$ increases, the bounds tighten and converge to the capacity with a vanishing gap of $O(N)$. For any EH probability parameter $etain {0.1,0.2, dots, 0.9}$, we compute the capacity with a precision of ${1e-6}$, outperforming the best-known bounds in the literature. Finally, we extend this framework to noisy EH channels with feedback, and present numerical achievable rates for the binary symmetric channel using a Markov decision process.

Problem

• Determine binary energy harvesting channel capacity
• Utilize convex optimization for precision
• Extend framework to noisy channels with feedback

Innovation

• Convex optimization for capacity precision
• Finite-state channel with causal state information
• Q-graphs for single-letter capacity bounds