The problem of transmitting a common message to multiple users over the Gaussian multiple-input multiple-output broadcast channel is considered, where each user is equipped with an arbitrary number of antennas. A closed-loop scenario is assumed, for which a practical capacity-approaching scheme is developed. By applying judiciously chosen unitary operations at the transmit and receive nodes, the channel matrices are triangularized so that the resulting matrices have equal diagonals, up to a possible multiplicative scalar factor. This, along with the utilization of successive interference cancellation, reduces the coding and decoding tasks to those of coding and decoding over the single-antenna additive white Gaussian noise channel. Over the resulting effective channel, any off-the-shelf code may be used. For the two-user case, it was recently shown that such joint unitary triangularization is always possible. In this paper, it is shown that for more than two users, it is necessary to carry out the unitary linear processing jointly over multiple channel uses, i.e., space-time processing is employed. It is further shown that exact triangularization, where all resulting diagonals are equal, is still not always possible, and appropriate conditions for the existence of such are established for certain cases. When exact triangularization is not possible, an asymptotic construction is proposed, that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small, at the price of processing a sufficiently large number of channel uses together.

It has long been known that linear codes achieve the capacity of additive channels over finite fields. Much less has been known about the performance of linear codes over Zm, when used for communication over channels that are additive with respect to this group. Further, linear codes over Zmplay an important role in construction of lattices in Euclidean space. When a construction-A lattice is used for communication over an additive white Gaussian noise channel, a modulo-MZ additive channel with unimodal noise is induced at the receiver. In this paper it is shown that linear codes over Zmachieve the capacity of such channels when the cardinality of the alphabet is a power of a prime.

We address the problem of communication over arbitrarily permuted parallel Gaussian channels, where the permutation is known only to the receiver. We present a practical transmission scheme, that allows to transmit over this channel using off-the-shelf codes, in conjunction with linear processing and successive interference cancellation. The scheme is based on the approach of joint matrix triangularization. Explicit precoding matrices are derived for up to six parallel channels.

Multicasting is the general method of conveying the same information to multiple users over a broadcast channel. In this work, the Gaussian MIMO broadcast channel is considered, with multiple users and any number of antennas at each node. A “closed loop” scenario is assumed, for which a practical capacity-achieving multicast scheme is constructed. In the proposed scheme, linear modulation is carried over time and space together, which allows to transform the problem into that of transmission over parallel scalar sub-channels, the gains of which are equal, except for a fraction of sub-channels that vanishes with the number of time slots used. Over these sub-channels, off-the-shelf fixed-rate AWGN codes can be used to approach capacity.

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.