The fifth generation (5G) wireless networks are expected to provide a wide range of time-sensitive multimedia services and applications to satisfy users' stringent requirements on delay-bounded quality of service (QoS). Finite blocklength coding theory can efficiently address the issue of delay-bounded QoS constraint guarantees, where mobile users send messages using packets with small numbers of bits to achieve low latency transmissions. In this paper, we employ the Nakagami-m fading model to analyze channel coding performance in the finite blocklength regime, in terms of average block error rate, capacity outage probability, and symbol error probability. We first derive closed-form expressions for upper and lower bounds on the average block error rate. Then, we compare these bounds with the capacity outage probability and show that the average block error rate is larger than the capacity outage probability. We also obtain a lower-bound in closed-form for the symbol error probability under M-ary phase shift keying (MPSK). Finally, we validate and evaluate our derived average block error rate bound, capacity outage probability, and symbol error probability in the finite blocklength regime through numerical analyses.