In 3GPP (3rd Generation Partnership Project) LTE (Long Term Evolution) systems, when HARQ (Hybrid Automatic Repeat request) retransmission is invoked, the data at the transmitter are retransmitted randomly or sequentially regardless of their relationship to the wrongly decoded data. Such practice is inefficient since precious transmission resources will be spent to retransmit data that may be of no use in error correction at the receiver. This paper proposes an incremental redundancy HARQ scheme based on Error Position Estimating Coding (ePec) and LDPC (Low Density Parity Check Code) channel coding, which is called ePec-LDPC HARQ. The proposal is able to feedback the wrongly decoded code blocks within a specific MAC (Media Access Control) PDU (Protocol Data Unit) from the receiver. The transmitter gets the feedback information and then performs targeted retransmission. That is, only the data related to the wrongly decoded code blocks are retransmitted, which can improve the retransmission efficiency and thus reduce the retransmission overload. An enhanced incremental redundancy LDPC coding approach, called EIR-LDPC, together with a physical layer framing method, is developed to implement ePec-LDPC HARQ. Performance evaluations show that ePec-LDPC HARQ reduces the overall transmission resources by 15% compared to a conventional LDPC HARQ scheme. Moreover, the average retransmission times of each MAC PDU and the transmission delay are also reduced considerably.