A data storage device is disclosed comprising a storage medium. Input data is encoded according to at least one channel code constraint to generate first data and second data. The first data is encoded into a first codeword, and the second data is encoded into a second codeword, wherein a first code rate of the first codeword is less than a second code rate of the second codeword. The first codeword and the second codeword are interleaved to generate an interleaved codeword, and the interleaved codeword is written to the storage medium.