In this paper, we propose a concatenated code by combining a Recursive Systematic Convolutional (RSC) code with a Low-Density Parity-Check (LDPC) code. The proposed concatenated code is encoded in parallel by an RSC encoder and an LDPC encoder without interleavers between them. When decoding the proposed concatenated code, the information bits are decoded by two decoding algorithms, and soft information is exchanged between the RSC decoder and the LDPC decoder. This allows for the elimination of wrong codewords output by each decoder. The use of an LDPC code allows us to halt the decoding process when the valid codeword is obtained. We evaluate the error rate performance of the proposed concatenated code by computer simulations. We show that the proposed concatenated code does not have a high error floor, and achieves better BLock Error Rate (BLER) performance than either conventional LDPC codes or conventional turbo codes in the high Eb/No region. We also show that since the proposed concatenated code can correct wrong codewords output by each decoder, it achieves better BLER than the regular LDPC code at the same Bit Error Rate (BER).