  This paper theoretically characterizes the degrees-of-freedom (DoF) region of
order-$(K-1)$ messages for the $K$-user multiple-input multiple-output (MIMO)
broadcast channel with delayed channel state information at the transmitter
(CSIT) and arbitrary antenna configurations, where the transmitter has $M$
antennas and the receiver $i=1,2,\cdots,K$ has $N_i$ antennas. For the
converse, we first derive the DoF region of order-$(K-1)$ messages for the
$K$-user MIMO broadcast channel with no CSIT and arbitrary antenna
configurations with the aid of the proposed Genie-bound, and then establish the
DoF outer region. For the achievability, we first design a 2-phase transmission
scheme, and then propose a backward/forward cancellation algorithm for
decoding. Specifically, we efficiently derive the achievable DoF region from
the designed transmission scheme by transformation approach. The main
implication of this paper is that for the order-$(K-1)$ messages of $K$-user
MIMO broadcast channel, the DoF region with delayed CSIT is larger than the DoF
region with no CSIT when $N_2<M$, where $N_1 \le N_2 \le \cdots \le N_K$.
