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A minimum mean-square error (MMSE)-based iterative soft interference cancellation (MMSE-SIC) receiver has been proposed to mitigate the interferences of the multiple-input multiple-output (MIMO) channels, with reduced complexity as compared to maximum-likelihood (ML) detection. On the other hand, the block-iterative generalized decision-feedback equalizer (BI-GDFE) attains close to the performance of the MMSE-SIC receivers with further reduced complexity. The BI-GDFE, however, requires an accurate estimate of the input-decision correlation (IDC), which is a statistical reliability metric of earlier-made decisions. To date, the BI-GDFE receiver is applicable only to phase-shift-keying (PSK) modulations due to the absence of a method to estimate the IDC for higher order quadrature amplitude modulations (QAMs). In this paper, we establish the relationship between the MMSE-SIC and BI-GDFE receivers and propose an algorithm to determine the IDC for BI-GDFE from the unconditional MMSE-SIC (U-MMSE-SIC). We further analyze and compare the asymptotic performances of the two receivers for large random MIMO channels and prove that for the limiting case, the output signal-to-interference-plus-noise ratios (SINRs) at each iteration for both receivers converge in probability to their respective deterministic limits. Our simulation results have shown that the bit error rate (BER) performance of the BI-GDFE receiver with the proposed IDC selection method achieves close to that of the U-MMSE-SIC receiver with similar convergence behavior and reaches the single-user matched filter bound (MFB) with several iterations for high enough signal-to-noise ratio (SNR).