  We investigate the non-orthogonal coexistence between the ultra-reliable
low-latency communication (URLLC) and the enhanced mobile broadband (eMBB) in
the downlink of a cell-free massive multiple-input multiple-output (MIMO)
system. We provide a unified information-theoretic framework that combines a
finite-blocklength analysis of the URLLC error probability based on the use of
mismatched decoding with an infinite-blocklength analysis of the eMBB spectral
efficiency. Superposition coding and three levels of puncturing are considered
as alternative downlink coexistence strategies to cope with the inter-service
interference and the URLLC random activation pattern, under the assumption of
imperfect pilot-based channel state information acquisition at the access
points and statistical channel knowledge at the users. Numerical results shed
light into the trade-off between eMBB and URLLC performances considering
different precoding and power control strategies.
