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We propose a list-based soft demodulator for MIMO systems that generates the soft information by solving a single semidefinite program (SDP). The computational cost of solving this SDP is guaranteed to be a (low-order) polynomial in the problem size, whereas existing list-based demodulators that employ sphere decoding principles do not have such a guarantee. The proposed demodulator also has a computational advantage over an existing semidefinite- relaxation-based soft demodulator that requires the solution of several SDPs. Our simulation results suggest that these computational advantages are achieved without incurring a significant degradation in performance.