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 − 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.
In this paper, we consider single-and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the additive white Gaussian noise (AWGN) channel with feedback under the average error probability formalism. By drawing ideas from Gallager and Nakiboglu's work for the direct part and the meta-converse for the converse part, we establish the ε-capacity and show that it depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that for any positive integer L, the second-order term is bounded between a term proportional to − ln (L) n (where ln (L) (·) is the L-fold nested logarithm function) and a term proportional to + √ n ln n where n is the blocklength. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available. In our second contribution, we establish the ε-capacity region for the AWGN multiple access channel (MAC) with feedback under the expected power constraint by combining ideas from hypothesis testing, information spectrum analysis, Ozarow's coding scheme, and power control.
This paper investigates the asymptotic expansion for the size of block codes defined for the additive white Gaussian noise (AWGN) channel with feedback under the following setting: A peak power constraint is imposed on every transmitted codeword, and the average error probability of decoding the transmitted message is non-vanishing as the blocklength increases. It is well-known that the presence of feedback does not increase the first-order asymptotics (i.e., capacity) in the asymptotic expansion for the AWGN channel. The main contribution of this paper is a selfcontained proof of an upper bound on the asymptotic expansion for the AWGN channel with feedback. Combined with existing achievability results for the AWGN channel, our result implies that the presence of feedback does not improve the second-and third-order asymptotics. An auxiliary contribution is a proof of the strong converse for the parallel Gaussian channels with feedback under a peak power constraint.
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