A Global Coding Scheme for OFDM over Finite Fields
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914551721623552 |
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| author | Li, Juane Yu, Qi-yue Abdel-Ghaffar, Khaled Lin, Shu |
| author_facet | Li, Juane Yu, Qi-yue Abdel-Ghaffar, Khaled Lin, Shu |
| contents | This paper proposes a highly efficient global coded-multiplexing scheme, conceptualized as Orthogonal Frequency Division Multiplexing over a finite field (FF-OFDM), for reliable multiuser communications. By utilizing a prime length cyclic code and its Hadamard equivalents as algebraic subcarriers, independent data streams are globally multiplexed via a Galois Fourier Transform (GFT) without rate loss. We show that this finite-field synthesis intrinsically generates a global Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code over $\mathrm{GF}(2^s)$, whose parity-check matrix is governed by the structural rigor of partial geometries. At the receiver, supported by a binary decomposition theorem, the received nonbinary global codeword is jointly decoded using parallel binary iterative soft-decision algorithms prior to demultiplexing. This joint decoding enables seamless reliability information sharing across all user streams, achieving near-bound error performance, rapid convergence without error floors, and strictly linear amortized decoding complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Global Coding Scheme for OFDM over Finite Fields Li, Juane Yu, Qi-yue Abdel-Ghaffar, Khaled Lin, Shu Information Theory This paper proposes a highly efficient global coded-multiplexing scheme, conceptualized as Orthogonal Frequency Division Multiplexing over a finite field (FF-OFDM), for reliable multiuser communications. By utilizing a prime length cyclic code and its Hadamard equivalents as algebraic subcarriers, independent data streams are globally multiplexed via a Galois Fourier Transform (GFT) without rate loss. We show that this finite-field synthesis intrinsically generates a global Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code over $\mathrm{GF}(2^s)$, whose parity-check matrix is governed by the structural rigor of partial geometries. At the receiver, supported by a binary decomposition theorem, the received nonbinary global codeword is jointly decoded using parallel binary iterative soft-decision algorithms prior to demultiplexing. This joint decoding enables seamless reliability information sharing across all user streams, achieving near-bound error performance, rapid convergence without error floors, and strictly linear amortized decoding complexity. |
| title | A Global Coding Scheme for OFDM over Finite Fields |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.09865 |