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We consider large MIMO systems, where by 'large' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas in V-BLAST (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just 0(NtNr), where Nt and Nr denote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas V-BLAST system with a high spectral efficiency of 200 bps/Hz (using BPSK and rate-1/3 turbo code), our simulation results show that the proposed detector performs close to within about 4.6 dB of the theoretical capacity. We also adopt the proposed detector for the low-complexity decoding of high-rate non-orthogonal space- time block codes (STBC) from division algebras (DA). We have decoded the 16x16 full-rate STBC from DA using the proposed detector and show that it performs close to within about 5.5 dB of the capacity using 4-QAM and rate-3/4 turbo code at a spectral efficiency of 24 bps/Hz. The practical feasibility of the proposed high-performance low-complexity detector could trigger wide interest in the implementation of large MIMO systems.