The Design of Rate-Compatible Structured Low-Density Parity-Check Codes
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The main objective of our research is to design practical low-density parity-check (LDPC) codes which provide a wide range of code rates in a rate-compatible fashion. To this end, we first propose a rate-compatible puncturing algorithm for LDPC codes at short block lengths (up to several thousand symbols). The proposed algorithm is based on the claim that a punctured LDPC code with a smaller level of recoverability has better performance. The proposed algorithm is verified by comparing performance of intentionally punctured LDPC codes (using the proposed algorithm) with randomly punctured LDPC codes. The intentionally punctured LDPC codes show better bit error rate (BER) performances at practically short block lengths. Even though the proposed puncturing algorithm shows excellent performance, several problems are still remained for our research objective. First, how to design an LDPC code of which structure is well suited for the puncturing algorithm. Second, how to provide a wide range of rates since there is a puncturing limitation with the proposed puncturing algorithm. To attack these problems, we propose a new class of LDPC codes, called efficiently-encodable rate-compatible (E2RC) codes, in which the proposed puncturing algorithm concept is imbedded. The E2RC codes have several strong points. First, the codes can be efficiently encoded. We present low-complexity encoder implementation with shift-register circuits. In addition, we show that a simple erasure decoder can also be used for the linear-time encoding of these codes. Thus, we can share a message-passing decoder for both encoding and decoding in transceiver systems that require an encoder/decoder pair. Second, we show that the non-systematic parts of the parity-check matrix are cycle-free, which ensures good code characteristics. Finally, the E2RC codes having a systematic rate-compatible puncturing structure show better puncturing performance than any other LDPC codes in all ranges of code rates. The throughput performance of incremental redundancy (IR) hybrid automatic repeat request (HARQ) systems highly depends on the performance of high-rate codes. Since the E2RC codes show excellent puncturing performance in all ranges of code rates, especially at high puncturing rate, we verify that E2RC codes outperform in throughput than other LDPC codes in IR-HARQ systems.