The throughput of a conventional rate-compatible code based hybrid automatic repeat request (HARQ) protocol is lower-bounded by the rate of the mother code used. The mother code rate along with the highest puncture rate determine the operation range of the protocol in terms of the average received signal-to-noise ratio (SNR). In this paper, we propose a new HARQ protocol based on rate-compatible punctured and shortened low-density parity-check (LDPC) code so that it admits a large operating SNR range. The large dynamic coding rate range is also useful for link adaptation applications. A distinct feature of the new HARQ protocol is: when a packet (frame) fails to pass the cyclic redundancy check (CRC) test and the system is operating at a rate lower than that of the mother code, the corresponding re-transmitted packet will consists of a coded payload resulted from systematic encoding a fraction of the CRC-failed bits plus new data bits. The re-encoded part plays the role of bridging two (component) codes, or equivalently, building a larger code out of smaller codes. Various decoding schedules that exchange messages between two or among more packets (component codes) become available and much decoding performance improvement can be obtained. Numerical results show that, compared with the conventional HARQ protocol, our approach provides significant better throughput performance in the low SNR region.