Non-Asymptotic Achievable Rates for Gaussian Energy-Harvesting Channels: Best-Effort and Save-and-Transmit
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An additive white Gaussian noise (AWGN) energy-harvesting (EH) channel is considered where the transmitter is equipped with an infinite-sized battery which stores energy harvested from the environment. The energy arrival process is modeled as a sequence of independent and identically distributed (i.i.d.) random variables. The capacity of this channel is known and is achievable by the so-called best-effort and save-and-transmit schemes. This paper investigates the best-effort scheme in the finite blocklength regime, and establishes the first non-asymptotic achievable rate for it. The first-order term of the non-asymptotic achievable rate equals the capacity, and the second-order term is proportional to -√( n/n) where n is the blocklength. The proof technique involves analyzing the escape probability of a Markov process. In addition, we use this new proof technique to analyze the save-and-transmit and derive a new non-asymptotic achievable rate for it, whose first-order and second-order terms achieve the capacity and the scaling -O(√(1/n)) respectively. For all sufficiently large signal-to-noise ratios (SNRs), this new achievable rate outperforms the existing ones. The results are also extended to the block energy arrival model where the length of each energy block L grows sublinearly in n. It is shown that best-effort and save-and-transmit achieve the second-order scalings -O(√({ n, L}/n)) and -O(√(L/n)) respectively.
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