The Reliability-Based Hybrid ARQ (RB-HARQ) scheme, which can be used with error correcting codes using soft-input soft-output (SISO) decoders such as convolutional codes and turbo codes, has been proposed. In the RB-HARQ scheme, the error rate performance is improved by selecting retransmission bits based on Log Likelihood Ratio (LLR) of each bit in the receiver. However, the receiver has to send the bit positions of retransmission bits to the transmitter. Therefore, the RB-HARQ scheme requires a large number of feedback bits. On the other hand, Low Density Parity Check (LDPC) codes are recently attracting a lot of interest, because LDPC codes can achieve near Shannon limit performance. In this paper, we evaluate the RB-HARQ scheme using LDPC codes. Moreover, we propose a RB-HARQ scheme that requires a fewer feedback bits by utilizing a code structure of LDPC code. We refer to the scheme as the RB-HARQ (row base) scheme. We show that the RB-HARQ and RB-HARQ (row base) schemes using LDPC codes have better error rate performance and higher throughput performance than no ARQ scheme. We also show that the RBHARQ (row base) scheme has a good trade-off between error rate performance and the number of feedback bits compared to the RB-HARQ scheme.