Information Freshness and Energy Harvesting Tradeoff in Network-Coded Broadcasting

Abstract

This letter investigates both information freshness and energy harvesting (EH) in downlink information update systems. Information freshness is characterized by age of information (AoI). We consider a scenario in which a large update message is packetized into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> small packets and encoded by random linear network coding (RLNC). A base station continuously broadcasts the RLNC-encoded packets to multiple users until all the users have received the message. When a user successfully receives the update message while at least one other user has not received it yet, the user harvests energy from the received signals. A key challenge is to decide the value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> in the message packetization in order to achieve low AoI and high EH simultaneously. To this end, we conduct a theoretical analysis of the tradeoff between the AoI and EH performance under different values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> . In particular, the packet error rates of short packets in the message packetization are estimated by the short packet theory, and the closed-form AoI and EH formulas are derived. Our numerical results reveal that there exists a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> (neither too small nor too large) that can achieve both low AoI and high EH.