Coded Status Updates in an Energy Harvesting Erasure Channel

We consider an energy harvesting transmitter sending status updates to a receiver over an erasure channel, where each status update is of length $k$ symbols. The energy arrivals and the channel erasures are independent and identically distributed (i.i.d.) and Bernoulli distributed in each slot. In order to combat the effects of the erasures in the channel and the uncertainty in the energy arrivals, we use channel coding to encode the status update symbols. We consider two types of channel coding: maximum distance separable (MDS) codes and rateless erasure codes. For each of these models, we study two achievable schemes: best-effort and save-and-transmit. In the best-effort scheme, the transmitter starts transmission right away, and sends a symbol if it has energy. In the save-and-transmit scheme, the transmitter remains silent in the beginning in order to save some energy to minimize energy outages in future slots. We analyze the average age of information (AoI) under each of these policies. We show through numerical results that as the average recharge rate decreases, MDS coding with save-and-transmit outperforms all best-effort schemes. We show that rateless coding with save-and-transmit outperforms all the other schemes.