Non-Asymptotic Achievable Rates for Energy-Harvesting Channels using Save-and-Transmit

TL;DR

This paper derives finite blocklength achievable rates for energy-harvesting channels using a save-and-transmit strategy, revealing that the rates approach channel capacity with a specific backoff term related to blocklength.

Contribution

It provides the first non-asymptotic lower bounds on achievable rates for EH channels, incorporating the save-and-transmit method and finite blocklength analysis.

Findings

Achievable rates approach capacity with a backoff proportional to -√(log n / n)

The first-order term of the rate matches the channel capacity C

The backoff constant is explicitly characterized and interpreted

Abstract

This paper investigates the information-theoretic limits of energy-harvesting (EH) channels in the finite blocklength regime. The EH process is characterized by a sequence of i.i.d. random variables with finite variances. We use the save-and-transmit strategy proposed by Ozel and Ulukus (2012) together with Shannon's non-asymptotic achievability bound to obtain lower bounds on the achievable rates for both additive white Gaussian noise channels and discrete memoryless channels under EH constraints. The first-order terms of the lower bounds of the achievable rates are equal to $C$ and the second-order (backoff from capacity) terms are proportional to $-\sqrt{ \frac{\log n}{n}}$, where $n$ denotes the blocklength and $C$ denotes the capacity of the EH channel, which is the same as the capacity without the EH constraints. The constant of proportionality of the backoff term is found and qualitative interpretations are provided.