We consider a joint Slepian-Wolf/Dirty-paper coding (SW-DPC) setup where a binary source needs to be transmitted over an additive white-Gaussian channel in the presence of interference known only at the encoder, as well as correlated side-information available only at the decoder. We propose a practical joint SW-DPC framework that uses a single low-density parity-check code coupled with trellis coded quantization to simultaneously provide error protection (in the face of noise and interference) and compression (in the face of correlated side-information available at the decoder). Simulation results indicate that the proposed joint SW-DPC scheme with finite-length codes outperforms a scheme with separate SW and DPC by 0.3 dB. In addition, we show that our joint SW-DPC code designed for one set of channel conditions is capable of achieving negligible bit-error rates for many other channel conditions as well. More specifically, it achieves successful decoding for a wide variety of channel conditions for which a separation-based scheme fails.