Optimal successive group decoder for the slow-fading multiple access channel

We consider a slow-fading narrowband multiple access channel (MAC) in which multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver knows it perfectly and employs the successive group decoder (SGD). We obtain achievable outage probabilities for the case where an outage must be declared simultaneously for all users (common outage) as well as the case where outages can be declared individually for each user (individual outage). We then derive the optimum successive group decoder (OSGD) which simultaneously minimizes the common outage probability and the individual outage probability of each user, over all successive group decoders of permissible decoding complexity. For each channel realization, the OSGD is also shown to maximize the minimum of the per-user error exponents of all users not in outage. An adaptive SGD is derived which retains the outage optimality of the OSGD but also minimizes the expected decoding complexity. Asymptotically tight affine approximations are then obtained for the weighted sum common and individual outage capacities and the symmetric outage capacities. Simulation results with practical LDPC outer codes show that the OSGD results in greatly improved performance at low decoding complexities.