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Binary low-density parity-check (LDPC) codes perform very well on magnetic recording channels (MRCs) with additive white Gaussian noise (AWGN). However, an MRC is subject to other impairments, such as media defects and thermal asperities. Binary LDPC codes may not be able to cope with these impairments without the help of a Reed-Solomon code. A better form of coding may be Q-ary LDPC codes, which have been shown to outperform binary LDPC codes and Reed-Solomon codes on the AWGN channel. In this paper, we report on our investigation of Q-ary LDPC coded MRCs, both with AWGN and with burst impairments, and we present a new reduced-complexity decoding algorithm for Q-ary LDPC codes. We show that Q-ary LDPC codes outperform binary LDPC codes in the presence of burst impairments.