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arXiv · 2605.09865

A Global Coding Scheme for OFDM over Finite Fields

Juane Li·Qi-yue Yu·Khaled Abdel-Ghaffar·Shu Lin
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Abstract

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.

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Juane Li, Qi-yue Yu, Khaled Abdel-Ghaffar, Shu Lin. 2026-05-11. A Global Coding Scheme for OFDM over Finite Fields. https://arxiv.org/abs/2605.09865

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