Minimum-Energy and Error-Rate for URLLC Networks over Nakagami-m Channels: A Finite-Blocklength Analysis

The fifth generation (5G) wireless networks aim at providing a wide range of time-sensitive multimedia services and applications to satisfy users’ stringent requirements on delay-bounded quality of service (QoS). One of the important requirements for 5G multimedia wireless networks is to efficiently support the ultra-reliable and low- latency communications (URLLC). Finite blocklength coding (FBC) is a promising candidate technique to support URLLC services, where mobile users transmit short packets to upper-bound the transmission delay of multimedia traffic. In this paper, we model and analyze the packet-block error rate for URLLC under the Nakagamim fading channel in the finite blocklength regime. Then, we derive the minimum energy per bit for data transmissions in the Nakagami-m fading channel under the constraint of block error rate. To derive closed-form expressions for the minimum energy per bit, we obtain achievability and converse bounds on the minimum energy per bit, and show that these two bounds are equal to each other. Finally, we evaluate our derived minimum energy per bit in the finite blocklength regime through numerical analyses, and compare it with those under the Rayleigh fading channel and the wideband approximation, validating our derived analytical results.