Source coding with correlated decoder side information is considered. We impose the practical constraint that the encoder be unaware of even the statistical dependencies between source and side information. Two classes of rate-adaptive distributed source codes, both based on low-density parity-check (LDPC) codes, are developed and their design is studied. Specific realizations are shown to be better than alternatives of linear encoding and decoding complexity. The proposed rate-adaptive LDPC accumulate (LDPCA) codes and sum LDPC accumulate (SLDPCA) codes (of length 6336 bits) perform within 10% and 5% of the Slepian-Wolf bound in the moderate and high rate regimes, respectively.