  In this paper, we study the multiple-antenna wireless communication networks,
where a large number of devices simultaneously communicate with an access
point. The capacity region of multiple-input multiple-output massive multiple
access channels (MIMO mMAC) is investigated. While joint typicality decoding is
utilized to establish the achievability of capacity region for conventional MAC
with fixed number of users, the technique is not directly applicable for MIMO
mMAC. Instead, an information-theoretic approach based on Gallager's error
exponent analysis is exploited to characterize the
\textcolor[rgb]{0,0,0}{finite dimension region} of MIMO mMAC. Theoretical
results reveal that the finite dimension region of MIMO mMAC is dominated by
sum rate constraint only, and the individual user rate is determined by a
specific factor that corresponds to the allocation of sum rate. The rate in
conventional MAC is not achievable with massive multiple access, which is due
to the fact that successive interference cancellation cannot guarantee an
arbitrary small error decoding probability for MIMO mMAC. The results further
imply that, asymptotically, the individual user rate is independent of the
number of transmit antennas, and channel hardening makes the individual user
rate close to that when only statistic knowledge of channel is available at
receiver. The finite dimension region of MIMO mMAC is a generalization of the
symmetric rate in Chen \emph{et al.} (2017).
