On Achievable Rates of AWGN Energy-Harvesting Channels With Block Energy Arrival and Non-Vanishing Error Probabilities

• Published in: IEEE transactions on information theory Vol. 64; no. 3; pp. 2038 - 2064
• Main Authors: Fong, Silas L., Tan, Vincent Y. F., Ozgur, Ayfer
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Achievable rates; Asymptotic series; AWGN channels; block energy arrival; Codes; Coherence; Continuity (mathematics); Distribution functions; Electronic mail; Encoding; Energy; Energy conservation; Energy harvesting; Energy transmission; Error analysis; Error probability; Gaussian process; Lower bounds; non-vanishing error probabilities; Random noise; Random variables; save-and-transmit; Upper bound; Upper bounds
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2017.2765545

This paper investigates the achievable rates of an additive white Gaussian noise energy-harvesting (EH) channel with an infinite battery. The EH process is characterized by a sequence of blocks of harvested energy, which is known causally at the source. The harvested energy remains constant within a block while the harvested energy across different blocks is characterized by a sequence of independent and identically distributed random variables. The blocks have length <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>, which can be interpreted as the coherence time of the energy-arrival process. If <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> is a constant or grows sublinearly in the blocklength <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>, we fully characterize the first-order term in the asymptotic expansion of the maximum transmission rate subject to a fixed tolerable error probability <inline-formula> <tex-math notation="LaTeX">\varepsilon </tex-math></inline-formula>. The first-order term is known as the <inline-formula> <tex-math notation="LaTeX">\varepsilon </tex-math></inline-formula>-capacity. In addition, we obtain lower and upper bounds on the second-order term in the asymptotic expansion, which reveal that the second order term is proportional to <inline-formula> <tex-math notation="LaTeX">-({L/{n}})^{1/2} </tex-math></inline-formula> for any <inline-formula> <tex-math notation="LaTeX">\varepsilon </tex-math></inline-formula> less than 1/2. The lower bound is obtained through analyzing the save-and-transmit strategy. If <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> grows linearly in <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>, we obtain lower and upper bounds on the <inline-formula> <tex-math notation="LaTeX">\varepsilon </tex-math></inline-formula>-capacity, which coincide whenever the cumulative distribution function of the EH random variable is continuous and strictly increasing. In order to achieve the lower bound, we have proposed a novel adaptive save-and-transmit strategy, which chooses different save-and-transmit codes across different blocks according to the energy variation across the blocks.