Rate-Compatible QC-LDPC codes

Xia Wei

Rate-compatible quasi-cyclic low-density parity-check(QC-LDPC)codes were designed with two construction methods.The first technique is based on code division,where a high-rate mother code is progressively divided into lower and lower rates;the other one adopts fractional row combination to yield a range of higher and higher rates form a relative low-rate mother code.The two methods cover different ranges of rates.Simulation result shows that the performance of these constructed rate-compatible QC-LDPC codes is as good as that of single rate codes which is straightly constructed based on the primitive elements of finite fields.

Juane Li, Shu Lin, Khaled Abdel-Ghaffar +2 more

Song Zhang, Linhua Ma, Le Ru +3 more

A class of rate-compatible (RC) quasi-cycle low-density parity-check (QC-LDPC) codes that have linear encodable complexity and low error floor is presented. To ensure linear encoding complexity, a lower triangular (LT) form for the parity part of the mother parity-check matrix is designed. By the designed LT form, a recursive encoding strategy is proposed. This encoding strategy can achieve linear encodable complexity, which is completely proportional to the code length. To guarantee good performances for a wide range of code rates, a layered short-cycle optimization algorithm is designed to obtain good girth distribution, and a layered density evolution algorithm is used to optimize degree distributions of each code rate. Then, a class of RC QC-LDPC codes can be obtained by both extension and puncturing from the optimized QC-LDPC mother code with rate 1/2. Simulation results show that no error floor is exhibited for the proposed RC QC-LDPC codes at FER=10-5. The practical performance at BER=10-6shows a gap of about 1.477 dB to the Shannon limit.

Juane Li, Shu Lin, Khaled Abdel-Ghaffar +2 more

Yuanhua Liu

An improved extension method based on protograph extrinsic information transfer (PEXIT) charts is proposed to design rate‐compatible quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes with more flexible rates and better performance. The masking matrix of the highest‐rate code can first be constructed column by column to own the lowest decoding threshold. Then, an extension algorithm is proposed to obtain the masking matrices of lower‐rate codes with flexible rates. Finally, the base matrices with small amount of short cycles are designed and the parity‐check matrices of rate‐compatible QC‐LDPC codes are obtained through matrix extension. Simulations show that compared with the existing codes, the proposed codes have more flexible rates while achieving better performance.

Ivan B. Djordjević