  Application of the turbo principle to multiuser decoding results in an
exchange of probability distributions between two sets of constraints. Firstly,
constraints imposed by the multiple-access channel, and secondly, individual
constraints imposed by each users' error control code. A-posteriori probability
computation for the first set of constraints is prohibitively complex for all
but a small number of users. Several lower complexity approaches have been
proposed in the literature. One class of methods is based on linear filtering
(e.g. LMMSE). A more recent approach is to compute approximations to the
posterior probabilities by marginalising over a subset of sequences (list
detection). Most of the list detection methods are restricted to non-singular
systems. In this paper, we introduce a transformation that permits application
of standard tree-search methods to underdetermined systems. We find that the
resulting tree-search based receiver outperforms existing methods.
