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We show how low-density parity-check (LDPC) codes can be used to compress close to the Slepian-Wolf limit for correlated binary sources. Focusing on the asymmetric case of compression of an equiprobable memoryless binary source with side information at the decoder, the approach is based on viewing the correlation as a channel and applying the syndrome concept. The encoding and decoding procedures are explained in detail. The performance achieved is seen to be better than recently published results using turbo codes and very close to the Slepian-Wolf limit.