In this work, a simple doped accumulator (DACC)-assisted relay system is proposed by using bit-interleaved coded modulation with iterative decoding (BICM-ID). An extrinsic information transfer (EXIT) chart analysis shows that DACC keeps the convergence tunnel of the EXIT curves open until almost the (1, 1) point of the mutual information, which avoids the error floor. In the relay system, errors may happen in the source-relay link (intra-link), however, they are allowed in our proposed technique where the correlation knowledge between the source and the relay is exploited at the destination node. Strong codes are not needed and even the systematic source bits can be simply extracted at the relay even though the systematic part may contain some errors. Hence, the complexity of the relay can be significantly reduced, and thereby the proposed system is energy-efficient. Furthermore, the error probability of the intra-link can be estimated at the receiver by utilizing the a posteriori log-likelihood ratios (LLRs) of the two decoders, and it can be further utilized in the iterative processing. Additionally, we provide the analysis of different relay location scenarios and compare the system performances by changing the relay's location. The transmission channels in this paper are assumed to suffer from additive white Gaussian noise (AWGN) and block Rayleigh fading. The theoretical background of this technique is the Slepian-Wolf/Shannon theorem for correlated source coding. The simulation results show that the bit-error-rate (BER) performances of the proposed system are very close to theoretical limits supported by the Slepian-Wolf/Shannon theorem.