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) <inline-formula> <tex-math notation="LaTeX">$\mathrm {GF}(2^{q})$ </tex-math></inline-formula> extension of Raptor-like (RL) quasi-cyclic (QC) subclass of Low-Density...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10820840/ |
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| Summary: | This paper explores an efficient rate-adaptive error correction coding scheme with a nonbinary (NB) <inline-formula> <tex-math notation="LaTeX">$\mathrm {GF}(2^{q})$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$\mathrm {GF}(2^{q})$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$\mathrm {GF}(2^{q})$ </tex-math></inline-formula> is combined with adaptive <inline-formula> <tex-math notation="LaTeX">$2^{X}$ </tex-math></inline-formula>-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. |
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| ISSN: | 2169-3536 |