Construction of Efficient High-Rate Protograph QC-LDPC Codes by Joint EXIT Chart, PEG, AWD, and QC-NLACE Techniques

To obtain efficient channel codes with high power efficiency at moderate signal-to-noise ratios (SNRs), an efficient high-rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is optimally constructed. By an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base QC matrix template is generated with required code rate and length by the extrinsic information transfer (EXIT) chart for better decoding threshold. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive-edge-growth (PEG) algorithm is employed to find the optimized positions of the QC sub-matrices to obtain larger girth for better error floor performance. Moreover, an asymptotic weight distribution (AWD) is employed to keep a low-code-error floor for the code. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC oriented nested loop approximated cycle extrinsic message degree (QC-NLACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph to cut the error floor. Simulation results show that the codes produced by the proposed method show quite good bit-error-rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency brought by the high code rate, and the low complexity by the short code length. Moreover, a series of different rate-compatible LDPC codes can be generated from the same protograph framework with some variable node extensions, which significantly eases the code design. Therefore, the proposed code construction can be efficiently applied in the optimal construction of high-rate and short-length rate-compatible QC-LDPC codes with a high data rate and rational complexity, which makes the codes extremely suited for use in new-generation power-constrained wireless communications.