  In this paper, the average achievable rate and error probability of a
reconfigurable intelligent surface (RIS) aided systems is investigated for the
finite blocklength (FBL) regime. The performance loss due to the presence of
phase errors arising from limited quantization levels as well as hardware
impairments at the RIS elements is also discussed. First, the composite channel
containing the direct path plus the product of reflected channels through the
RIS is characterized. Then, the distribution of the received signal-to-noise
ratio (SNR) is matched to a Gamma random variable whose parameters depend on
the total number of RIS elements, phase errors and the channels' path loss.
Next, by considering the FBL regime, the achievable rate expression and error
probability are identified and the corresponding average rate and average error
probability are elaborated based on the proposed SNR distribution. Furthermore,
the impact of the presence of phase error due to either limited quantization
levels or hardware impairments on the average rate and error probability is
discussed. The numerical results show that Monte Carlo simulations conform to
matched Gamma distribution to received SNR for sufficiently large number of RIS
elements. In addition, the system reliability indicated by the tightness of the
SNR distribution increases when RIS is leveraged particularly when only the
reflected channel exists. This highlights the advantages of RIS-aided
communications for ultra-reliable and low-latency systems. The difference
between Shannon capacity and achievable rate in FBL regime is also discussed.
Additionally, the required number of RIS elements to achieve a desired error
probability in the FBL regime will be significantly reduced when the phase
shifts are performed without error.
