Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation

This paper explores an efficient rate-adaptive error correction coding scheme with a nonbinary (NB) $\mathrm {GF}(2^{q})$ extension of Raptor-like (RL) quasi-cyclic (QC) subclass of Low-Density Parity-Check (LDPC) codes. In the NB RL scheme, the high-rate (HR) code vectors are supplemented by the incremental redundancy (IR) symbols, generated by the parity check equations over $\mathrm {GF}(2^{q})$ . We provide a procedure for constructing short NB QC-RL-LDPC codes with low encoding complexity and optimized graph structures. The proposed method is based on the graph optimization of the HR code and Monte Carlo simulation-supported placement of additional NB parity checks in the IR graph. Numerical simulations validate the approach, demonstrating the effectiveness of the constructed short NB QC-RL-LDPC codes, compared to the 5G standard binary coding with IR. Further exploration shows that, when the NB QC-RL-LDPC coding over Galois Field $\mathrm {GF}(2^{q})$ is combined with adaptive $2^{X}$ -ary digital modulations, which provides flexibility in diversifying modulation orders by mixing higher order modulations for initial HR transmission with a lower order for IR, it can improve performance in the low Signal to Noise Ratio regime. In conclusion, this investigation shows that the Raptor-Like nonbinary coding, when the code and the transmission scheme are designed with proper optimizations, exhibits a performance improvement over the counterpart binary coding.