The present invention discloses methods and apparatuses for quantizing, and feeding back channel information and precoding data. In the above methods, a channel measurement pilot signal is received from a base station. The channel information is acquired by performing channel measurement according to the channel measurement pilot signal. CMatrix1 and CMatrix2 are calculated using the channel information, herein CMatrix1 and CMatrix2 are used to quantize the channel information or indicate the base station to perform precoding. And first indication information of CMatrix1 and/or second indication information of CMatrix2 are fed back to the base station. According to the technical solutions of the present invention, as the influence of the polarization leakage is considered in the feedback design, a significant performance gain exists in a case that the polarization leakage actually occurs.