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This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of k, the number of information bits. It is demonstrated that in this non-asymptotic regime, noiseless feedback leads to significantly better energy efficiency. In particular, without feedback achieving energy per bit of - 1.57 dB requires coding over at least k = 106 information bits, while the authors construct a feedback scheme that transmits a single information bit with energy ??'1.59 dB and zero error. They also show that unless k is very small, approaching the minimal energy per bit does not require using the feedback link except to signal that transmission should stop.
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