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Design of MIMO capacity-approaching codes relies on matching the extrinsic information transfer (EXIT) functions of the code and the detector. We focus on list sphere detection (LSD) because it presents the best performance/complexity tradeoff. We obtain the EXIT functions of the most representative LSDs: maximum likelihood (ML) and maximum a posteriori (MAP). We then utilize these EXIT functions to design good IRA and SCLDGM codes that perform close to the capacity limits.