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: Jakub Hyla, Wojciech Sulek
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Access
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Online Access:https://ieeexplore.ieee.org/document/10820840/
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author Jakub Hyla
Wojciech Sulek
author_facet Jakub Hyla
Wojciech Sulek
author_sort Jakub Hyla
collection DOAJ
description 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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spelling doaj-art-381fc812a5e24a94bc08c0bf59bc0d352025-08-20T02:46:46ZengIEEEIEEE Access2169-35362025-01-01133849386310.1109/ACCESS.2024.351717110820840Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and SimulationJakub Hyla0Wojciech Sulek1https://orcid.org/0000-0003-3462-0657TKH Technology Poland Sp. z.o.o., Leszno, PolandFaculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Gliwice, PolandThis 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.https://ieeexplore.ieee.org/document/10820840/Error correction codingLDPCnonbinary LDPCRaptor codingmodulation mapping
spellingShingle Jakub Hyla
Wojciech Sulek
Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation
IEEE Access
Error correction coding
LDPC
nonbinary LDPC
Raptor coding
modulation mapping
title Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation
title_full Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation
title_fullStr Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation
title_full_unstemmed Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation
title_short Short Blocklength Nonbinary Raptor-Like LDPC Coding Systems Design and Simulation
title_sort short blocklength nonbinary raptor like ldpc coding systems design and simulation
topic Error correction coding
LDPC
nonbinary LDPC
Raptor coding
modulation mapping
url https://ieeexplore.ieee.org/document/10820840/
work_keys_str_mv AT jakubhyla shortblocklengthnonbinaryraptorlikeldpccodingsystemsdesignandsimulation
AT wojciechsulek shortblocklengthnonbinaryraptorlikeldpccodingsystemsdesignandsimulation