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 @math and the second-order (backoff from capacity) terms are proportional to @math , where @math denotes the blocklength and @math 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.
We consider a binary energy harvesting channel (BEHC) where the encoder has unit energy storage capacity. We first show that an encoding scheme based on block indexing is asymptotically optimal for small energy harvesting rates. We then present a novel upper bounding technique, which upper bounds the rate by lower-bounding the rate of information leakage to the receiver regarding the energy harvesting process. Finally, we propose a timing based hybrid encoding scheme that achieves rates within 0:03 bits channel use of the upper bound; hence determining the capacity to within 0:03 bits channel use. I. INTRODUCTION We consider the problem of determining the capacity of an energy-harvesting transmitter with finite battery communicating over a discrete memoryless channel. When the battery is unlimited, or zero, the capacity has been determined, but it remains unknown for a finite non-zero battery. In this paper we assume that the harvested energy at each time, the total battery storage, and the transmitter signal energy at each time can be quantized to the same unit (i.e., the same energy interval). Under this assumption, we show that the capacity can be described using the Verdu-Han general framework. If we further assume that the transmitted symbol at each time depends only on the energy currently available, and not on the entire past history of energy harvests and symbols transmitted, then we show that the system reduces to a finite state channel (FSC) with the required ergodic and Markov properties so that lower bounds on the capacity can be readily numerically computed. We conjecture that our numerical bounds are tight. Our numerical results indicate that even the minimal possible battery storage can reap a significant fraction of the infinite battery capacity. A noiseless binary energy harvesting channel with on-off fading is considered. When causal fading state information is available at the transmitter only, an equivalent timing channel with additive geometric noise and noise information known at the transmitter is obtained. In this channel, the transmitter's strategy is a stopping rule with respect to the channel fade levels given the message and the additive noise. Next, capacity when energy arrival information is available at the receiver and capacity when both energy arrival and fading information are available at the receiver are obtained. Additionally, several achievable schemes are proposed and evaluated. We consider the capacity of an energy harvesting communication channel with a finite-sized battery. As an abstraction of this problem, we consider a system where energy arrives at the encoder in multiples of a fixed quantity, and the physical layer is modeled accordingly as a finite discrete alphabet channel based on this fixed quantity. Further, for tractability, we consider the case of binary energy arrivals into a unit-capacity battery over a noiseless binary channel. Viewing the available energy as state, this is a state-dependent channel with causal state information available only at the transmitter. Further, the state is correlated over time and the channel inputs modify the future states. We show that this channel is equivalent to an additive geometric-noise timing channel with causal information of the noise available at the transmitter. We provide a single-letter capacity expression involving an auxiliary random variable, and evaluate this expression with certain auxiliary random variable selection, which resembles noise concentration and lattice-type coding in the timing channel. We evaluate the achievable rates by the proposed auxiliary selection and extend our results to noiseless ternary channels. A formula for the capacity of arbitrary single-user channels without feedback (not necessarily information stable, stationary, etc.) is proved. Capacity is shown to equal the supremum, over all input processes, of the input-output inf-information rate defined as the liminf in probability of the normalized information density. The key to this result is a new converse approach based on a simple new lower bound on the error probability of m-ary hypothesis tests among equiprobable hypotheses. A necessary and sufficient condition for the validity of the strong converse is given, as well as general expressions for spl epsiv -capacity. >