On Lossy Joint Source-Channel Coding In Energy Harvesting Communication Systems

TL;DR

This paper investigates the limits of lossy joint source-channel coding in energy harvesting systems with battery leakage, deriving bounds, optimality conditions, and analyzing adaptive coding strategies for Gaussian and binary sources.

Contribution

It introduces a framework for adaptive joint source-channel coding considering energy constraints and leakage, with explicit formulas and optimality conditions for mismatch and power policies.

Findings

Derived a lower bound on achievable distortion.

Obtained closed-form mismatch factor for Gaussian sources.

Showed inverse relationship between power and mismatch factor policies.

Abstract

We study the problem of lossy joint source-channel coding in a single-user energy harvesting communication system with causal energy arrivals and the energy storage unit may have leakage. In particular, we investigate the achievable distortion in the transmission of a single source via an energy harvesting transmitter over a point-to-point channel. We consider an adaptive joint source-channel coding system, where the length of channel codewords varies based on the available battery charge. We first establish a lower bound on the achievable distortion. Then, as necessary conditions for local optimality, we obtain two coupled equations that determine the mismatch ratio between channel symbols and source symbols as well as the transmission power, both as functions of the battery charge. As examples of continuous and discrete sources, we consider Gaussian and binary sources respectively. For the Gaussian case, we obtain a closed-form expression for the mismatch factor in terms of the $Lambert W$ function, and show that an increasing transmission power policy results in a decreasing mismatch factor policy and vice versa. Finally, we numerically compare the performance of the adaptive mismatch factor scheme to the case of a constant mismatch factor.