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.
Mao and Hassibi @cite_22 investigated the capacity of an energy-harvesting transmitter with finite battery over a discrete memoryless channel (DMC). It was shown that the capacity can be described using the Verd 'u-Han general framework @cite_10 . If the transmitted symbol only depends on the currently available energy, the system reduced to a finite-state channel. However, it was analytically intractable to explicitly characterize the capacity, and even the lower bound of the capacity can only be evaluated numerically. A special scenario of the same problem, namely the capacity of noiseless binary channel with binary energy arrivals and unit-capacity battery, was discussed in @cite_5 . The channel was shown to be equivalent to an additive geometric-noise timing channel with causal information of the noise available at the transmitter. Achievable strategies were proposed along with upper bounds, which were then improved in @cite_4 . Ozel @cite_24 considered a noiseless binary energy harvesting channel with on-off fading.
@cite_4 @cite_22 @cite_24 @cite_5 @cite_10
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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. 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. We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an M-user AWGN broadcast channel where the transmitter is able to harvest energy from the nature, using a finite storage capacity rechargeable battery. The harvested energy is modeled to arrive (be harvested) at the transmitter during the course of transmissions at arbitrary time instants. The transmitter has fixed number of packets for each receiver. Due to the finite battery capacity, energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional water-filling algorithm. We prove that there exist M-1 cut-off power levels such that user i is allocated the power between the i-1st and the ith cut-off power levels subject to the availability of the allocated total power level. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional water-filling repetitively. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. 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.