In Multiple-Input Multiple-Output (MIMO) wireless systems, since different signals are transmitted by different antennas simultaneously, interference occurs between the transmitted signals. The receiver has to detect each signal from the multiplexed signal. MMSE-SIC combines MMSE filtering and Soft Interference Cancellation (SIC) with soft replicas and can achieve good Bit Error Rate (BER) performance. If an irregular LDPC code or a turbo code is used, the reliability and BER of the information bits output by the decoder are likely to be higher and better than the parity bits. In MMSE-SIC, bits with poor reliability lower the accuracy of soft replica estimation. When the soft replica is inaccurate, the gain obtained by SIC is small. For M-ary Phase Shift Keying (PSK) and M-ary Quadrature Amplitude Modulation (QAM), larger constellations such as 8PSK and 16QAM transfer more bits per symbol, and the number of bits per symbol impacts the accuracy of SIC. Unfortunately, increasing the number of bits per symbol is likely to lower the accuracy of soft replica estimation. In this paper, we evaluate three types of the mapping scheme for MMSE-SIC with either LDPC codes or turbo codes with the goal of effectively increasing the SIC gain. The first scheme is the information bit or the parity bit reliable mapping. In this scheme, either information bits or parity bits are assigned to strongly protected bits. The second scheme is the weight based mapping. When the number of information bits is larger than that of strongly protected bits, not all the information bits are assigned to strongly protected bits. In the weight based mapping, information bits are assigned to strongly protected bits with the increasing or decreasing orders of that weight. The last one is the random mapping. Computer simulations show that in MMSE-SIC with irregular LDPC codes or turbo codes, information reliable and high weight reliable mapping offer the highest SIC gain. We also show that in MMSE-SIC with the regular LDPC code, the gains offered by the mapping schemes are very small.