  In a recent work, a capacity-achieving scheme for the common-message two-user
MIMO broadcast channel, based on single-stream coding and decoding, was
described. This was obtained via a novel joint unitary triangularization which
is applied to the corresponding channel matrices. In this work, the
triangularization is generalized, to any (finite) number of matrices, allowing
multi-user applications. To that end, multiple channel uses are jointly
treated, in a manner reminiscent of space-time coding. As opposed to the
two-user case, in the general case there does not always exist a perfect
(capacity-achieving) solution. However, a nearly optimal scheme (with vanishing
loss in the limit of large blocks) always exists. Common-message broadcasting
is but one example of communication networks with MIMO links which can be
solved using an approach coined "Network Modulation"; the extension beyond two
links carries over to these problems.
