In this paper, a new adaptive distributed video coding (DVC) method with received motion vectors (MVs) through a back channel is proposed. The MVs estimated for side information (SI) generation in the proposed DVC decoder are transmitted to the proposed DVC encoder to reconstruct a predicted SI (PSI) which is the same as the SI at the decoder with minimum computational load. Therefore, the proposed DVC encoder can determine the positions and magnitudes of errors using the PSI. With available error information, the proposed encoder adaptively determines appropriate slice partitions by maintaining fixed per-slice error rates for prevention of channel decoding failure. The encoder also sends a coded SI accuracy map to the decoder and sets the conditional probability of each variable node of the low-density parity-check accumulator (LDPCA) to the correct crossover probability according to the coded map as received on the decoder side. The performance of the LDPCA can also be significantly improved with a minimum number of parity bits and low computational complexity because accurate belief propagation can be carried out using the correct crossover probabilities in the LDPCA decoder. Experimental results show that the rate-distortion performance of the proposed algorithm is twice that of several conventional DVC methods and that the proposed decoder is approximately 24.5% faster than these methods.