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A K-symmetric channel is a K-user linear multiple-access channel in which the cross correlations between each pair of users are identical. The main contribution of this correspondence is an algorithm which finds the P sequences with highest a posteriori probability (APP) in the case of binary transmission over a K-symmetric channel with additive white Gaussian noise. This list detector is applied to the problem of iterative multiple-user decoding, approximating the APP computation by marginalization over these P sequences, rather than all possible 2K sequences. Simulation results indicate that using only small values of P, very good performance may be obtained. It is also demonstrated how to incorporate prior probabilities (a requirement for iterative decoding). The overall per-bit computational complexity of the approach is O(K2+PlogP). It is also shown that for any multiuser system possessing a polynomial complexity optimal detection algorithm it is possible to obtain the P most probable sequences with polynomial complexity.