This paper investigates the achievable rates of an additive white Gaussian noise (AWGN) 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 (i.i.d.) random variables. The blocks have length @math , which can be interpreted as the coherence time of the energy arrival process. If @math is a constant or grows sublinearly in the blocklength @math , we fully characterize the first-order term in the asymptotic expansion of the maximum transmission rate subject to a fixed tolerable error probability @math . The first-order term is known as the @math -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 scales as @math for any @math less than @math . The lower bound is obtained through analyzing the save-and-transmit strategy. If @math grows linearly in @math , we obtain lower and upper bounds on the @math -capacity, which coincide whenever the cumulative distribution function (cdf) 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.
For a fixed tolerable error probability @math , @cite_10 recently performed a finite blocklength analysis of save-and-transmit schemes proposed in @cite_8 and obtained a non-asymptotic achievable rate for the AWGN channel with an i.i.d. EH process. The first-, second- and third-order terms of the non-asymptotic achievable rate presented in [Th. 1] FTY15 are equal to the capacity, @math and @math respectively where @math and @math are some positive constants that do not depend on @math and @math . Subsequently, Shenoy and Sharma @cite_5 refined the analysis in @cite_10 and improved the second-order term to @math where @math is some positive constant that does not depend on @math and @math . This paper further improves the second-order term to @math for any @math where @math is some positive constant that does not depend on @math and @math (see Remark ). The aforementioned improvements are due to better analyses of the energy outage" probability for the same save-and-transmit strategy, where the energy outage" occurs when the source cannot output the desired codeword due to energy shortage.
@cite_5 @cite_10 @cite_8
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We study the performance limits of state-dependent discrete memoryless channels with a discrete state available at both the encoder and the decoder. We establish the epsilon-capacity as well as necessary and sufficient conditions for the strong converse property for such channels when the sequence of channel states is not necessarily stationary, memoryless or ergodic. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels. 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. In energy harvesting communication systems, an exogenous recharge process supplies energy necessary for data transmission and the arriving energy can be buffered in a battery before consumption. We determine the information-theoretic capacity of the classical additive white Gaussian noise (AWGN) channel with an energy harvesting transmitter with an unlimited sized battery. As the energy arrives randomly and can be saved in the battery, codewords must obey cumulative stochastic energy constraints. We show that the capacity of the AWGN channel with such stochastic channel input constraints is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two capacity achieving schemes: save-and-transmit and best-effort-transmit. In the save-and-transmit scheme, the transmitter collects energy in a saving phase of proper duration that guarantees that there will be no energy shortages during the transmission of code symbols. In the best-effort-transmit scheme, the transmission starts right away without an initial saving period, and the transmitter sends a code symbol if there is sufficient energy in the battery, and a zero symbol otherwise. Finally, we consider a system in which the average recharge rate is time varying in a larger time scale and derive the optimal offline power policy that maximizes the average throughput, by using majorization theory.