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We discuss three structures of modified low-density parity-check (LDPC) code ensembles designed for transmission over arbitrary discrete memoryless channels. The first structure is based on the well-known binary LDPC codes following constructions proposed by Gallager and McEliece, the second is based on LDPC codes of arbitrary (q-ary) alphabets employing modulo-q addition, as presented by Gallager, and the third is based on LDPC codes defined over the field GF(q). All structures are obtained by applying a quantization mapping on a coset LDPC ensemble. We present tools for the analysis of nonbinary codes and show that all configurations, under maximum-likelihood (ML) decoding, are capable of reliable communication at rates arbitrarily close to the capacity of any discrete memoryless channel. We discuss practical iterative decoding of our structures and present simulation results for the additive white Gaussian noise (AWGN) channel confirming the effectiveness of the codes.