An operating method of a controller includes selecting bits of code word to be punctured; detecting locations of incapable bits of an input word based on locations of the bits to be punctured and a structure of a generation matrix calculation unit; refreezing the input word such that frozen bits and incapable bits of the input word overlap; generating input word bits by replacing information word bits with frozen bits based on the refreezing result; generating the code word by performing generation matrix calculation on the input word bits; generating output bits by puncturing the code word based on locations of the bits to be punctured; and transmitting the output bits to a nonvolatile memory device.