Coding For The Binary Energy Harvesting Channel With Finite Battery

In this paper, we give a framework for constructing codes over the binary energy harvesting channel when the energy arrivals are random and the battery has large but finite size. We study both noiseless and noisy binary channels (i.e., bit flips). In the noiseless case, we present an encoding strategy (called exponential backoff encoding) which uses a decreasing amount of energy in consecutive transmissions between energy arrivals. We analyze the achievable rate of backoff encoding and show that it can outperform a uniform energy usage policy. We then extend the encoding strategy to a noisy binary channel, suggest a corresponding decoder, and analyze its performance. We believe our constructive approach complements existing approaches which focus on the information capacity of energy harvesting channels.