Lossy Joint Source-Channel Coding for Energy Harvesting Communication Systems

In this work, we study the problem of lossy joint source-channel coding in an energy harvesting single-user communication system with causal energy arrivals, where the energy storage unit may have leakage. In particular, we investigate the achievable distortion in the transmission of a single source with arbitrary alphabets via an energy harvesting transmitter over a point-to-point channel. We first establish a lower bound on the achievable distortion. Then, to minimize the distortion we consider an adaptive joint source-channel coding scheme, where the length of channel codewords varies adaptively based on the available battery charge in each communication block. For this scheme, we obtain two coupled equations that determine the mismatch ratio between channel symbols and input symbols as well as the transmission power, both as functions of battery charge. As examples of continuous and discrete sources, we consider Gaussian and binary sources. In particular, for the Gaussian case, we obtain a closed form expression for the mismatch factor in terms of the LambertW function, and show that an increasing transmission power results in a decreasing mismatch factor and vice versa. We also numerically show that when the mismatch factor adaptively changes based on the available charge in the battery, the communication system achieves a smaller distortion compared to that of a constant mismatch factor.