  Cell-free massive multiple-input multiple-output (MIMO) is a promising
network to offer huge improvement of the achievable rate compared with
conventional cellular massive MIMO systems. However, the commonly adopted
Shannon-type achievable rate is only valid in the long block length regime that
is not applicable to the emerging short-packet communication. To realize
ultra-reliable and low-latency communication (URLLC) in cell-free massive MIMO
systems, we optimize the precoding vector at the access points (APs) to
maximize the minimum user rate in both the centralized and decentralized
fashion. The design takes into account the impact of URLLC and we propose
path-following algorithms (PFA) to address the considered problem which
generates a sequence of advanced feasible points and converges to at least a
locally optimal solution of the design problem. Moreover, we investigate the
requirement of the precoding schemes, the length of the transmission duration,
the number of antennas equipped at each AP, and the size of each AP cluster on
the URLLC rate. Numerical results show that the decentralized PFA precoding can
achieve 80\% of the 95\%-likely URLLC rate of the centralized precoding and
89\% of the average URLLC rate with only 12\% computational complexity of the
centralized precoding.
