This work investigates the energy-delay tradeoff in real-time network communication systems with ARQ, where energy is measured by power and energy per bit, respectively. We consider the lossy communication case with a finite buffer size, where each block is allowed to be retransmitted under a time constraint. We apply finite blocklength results of channel coding into our system. By adaptively optimizing the blocklength, coding rate, power allocation, and maximum number of retransmissions according to the queue state, we algorithmically achieve the optimal energy-delay tradeoff. We also lower and upper bound the optimal energy-delay function in order to study its asymptotic behavior as the delay and buffer size go to infinity, showing consistency with existing result. That is: the energy per bit approaches the minimum of −1.59 dB as the delay goes to infinity and power approaches zero. We observe that the power increases very rapidly when delay moves away from infinity, meaning that it is very hard to achieve the −1.59 dB limit in practice.
['Lei Yu', 'Houqiang Li', 'Weiping Li', 'Zixiang Xiong', 'Anders Host-Madsen']
On the energy-delay tradeoff in lossy network communications