arXiv subjects

Qi-yue Yu

Publications and source records attributed to Qi-yue Yu.

6 recordsLinked to original sources

arXiv2026

A Global Coding Scheme for OFDM over Finite Fields

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.

cs.IT↗

arXiv2025

Polarized Element-pair Code Based FFMA over a Gaussian Multiple-access Channel

This paper presents polarized element-pair (EP) codes for polarization-adjusted finite-field multiple-access (PA-FFMA) systems. The core innovation of FFMA systems lies in their unique processing order that exchanges the conventional sequence of channel coding and multiplexing operations, effectively solving the multiuser finite-blocklength (FBL) problem while enhancing error performance. In this architecture, EPs serve as virtual resources for user separation, where different EP codes provide distinct error performance characteristics. The proposed polarized EP code differs from classical polar codes in one aspect that it is specifically designed for Gaussian multiple access channel (GMAC) environments rather than single-user Gaussian channels. We derive the channel capacity for this polarized EP code based FFMA system, then develop an optimal power allocation scheme to maximize multiuser channel capacity. The code construction employs the Marto Loco method for selecting the polarized index set. For decoding, we introduce two specialized algorithms. A successive cancellation list (SCL) decoder for the balanced information-parity section scenarios, and a top $L$ bifurcated minimum distance (Top$L$-BMD) decoder for small payload cases while maintaining comparable error performance. Simulations show that, for $15$ users, our system achieves a $1.25$ dB coding gain compared to the state-of-the-art polar random spreading systems.

cs.IT↗

arXiv2025

Finite Field Multiple Access III: from 2-ary to p-ary

This paper extends finite-field multiple-access (FFMA) techniques from binary to general $p$-ary source transmission. We introduce element-assemblage (EA) codes over GF($p^m$), which generalize element-pair (EP) codes, and define two specific types for ternary transmission: orthogonal EA codes and double codeword EA (D-CWEA) codes. We propose a unique sum-pattern mapping (USPM) constraint for the design of uniquely-decodable CWEA (UD-CWEA) codes, which include additive inverse D-CWEA (AI-D-CWEA) and basis decomposition D-CWEA (BD-D-CWEA) codes. Additionally, we introduce non-orthogonal CWEA (NO-CWEA) codes and their corresponding USPM constraint in the complex field. Furthermore, $p$-ary CWEA codes are constructed using a basis decomposition method, leveraging ternary decomposition for faster convergence and simplified encoder/decoder design. We present a performance analysis of the proposed FFMA system from two complementary perspectives: channel capacity and error performance. We demonstrate that equal power allocation achieves the theoretical channel capacity, and then investigate the finite blocklength (FBL) characteristics of FFMA systems. Moreover, we develop a rate-driven capacity alignment (CA) theorem based on the capacity-to-rate ratio (CRR) metric for error performance analysis. Finally, we compare $p$-ary transmission systems with classical binary transmission systems, revealing that low-order $p$-ary systems (e.g., $p = 3$) outperform binary systems at small loading factors, while higher-order systems (e.g., $p = 257$) excel at larger loading factors. These findings highlight the potential of $p$-ary systems, although practical implementations may benefit from decomposing $p$-ary systems into ternary systems to manage complexity.

cs.IT↗

arXiv2025

Finite Field Multiple Access II:from Symbol-wise to Codeword-wise

A finite-field multiple-access (FFMA) system separates users within a finite field by utilizing different element-pairs (EPs) as virtual resources. The Cartesian product of distinct EPs forms an EP code, which serves as the input to a finite-field multiplexing module (FF-MUX). This allows the FFMA technique to reorder the channel coding and multiplexing modules, enabling the superimposed signals to function as codewords that can be decoded by a channel code. This flexibility allows the FFMA system to efficiently support a large number of users with short packet traffic, addressing the finite blocklength (FBL) challenge in multiuser reliable transmission. Designing EP codes is a central challenge in FFMA systems. In this paper, we construct EP codes based on a bit(s)-to-codeword transformation approach and define the corresponding EP code as a codeword-wise EP (CWEP) code. We then investigate the encoding process of EP codes, and propose unique sum-pattern mapping (USPM) structural property constraints to design uniquely decodable CWEP codes. Next, we present the $\kappa$-fold ternary orthogonal matrix ${\bf T}_{\rm o}(2^{\kappa}, 2^{\kappa})$ over GF$(3^m)$, where $m = 2^{\kappa}$, and the ternary non-orthogonal matrix ${\bf T}_{\rm no}(M,m)$ over GF$(3^m)$, for constructing specific CWEP codes. Based on the proposed CWEP codes, we introduce three FFMA modes: channel codeword multiple access (FF-CCMA), code division multiple access (FF-CDMA), and non-orthogonal multiple access (FF-NOMA). Simulation results demonstrate that all three modes effectively support massive user transmissions with well-behaved error performance.

cs.IT↗

arXiv2024

Finite Field Multiple Access for Sourced Massive Random Access with Finite Blocklength

For binary source transmission, this paper introduces the concept of element-pair (EP) and establishes that when the Cartesian product of $J$ distinct EPs satisfies the unique sum-pattern mapping (USPM) structural property, these $J$ EPs can form a uniquely-decodable EP (UD-EP) code. EPs are treated as virtual resources allocated to different users in finite fields, serving to distinguish users. This approach enables the reordering of multiplexing and channel encoding modules, effectively addressing the finite blocklength (FBL) challenge in multiuser reliable transmission. Next, we introduce an orthogonal EP code $\Psi_{\rm o, B}$ constructed over an extension field GF($2^m$). Using this EP code, we develop a time-division mode of finite-field multiple-access (FFMA) systems, consisting of sparse-form and diagonal-form structures. Based on the diagonal-form (DF) structure, we present a specific configuration, referred to as polarization-adjusted DF-FFMA, which can simultaneously obtain the power gain and coding gain from the entire blocklength. Simulation results demonstrate that the proposed FFMA systems significantly improve error performance over a Gaussian multiple-access channel, compared to a slotted ALOHA system.

cs.IT↗

arXiv2023

Finite Field Multiple Access

In the past several decades, various techniques have been developed and used for multiple-access (MA) communications. With the new applications for 6G, it is desirable to find new resources, physical or virtual, to confront the fast development of MA communication systems. For binary source transmission, this paper introduces the concept of element-pair (EP), and the Cartesian product of $J$ distinct EPs can form an EP code. EPs are treated as virtual resources in finite fields to distinguish users. This approach allows for the reordering of channel encoding and multiplexing modules, allowing superimposed signals to function as codewords decodable by a channel code, thereby effectively addressing the finite blocklength (FBL) challenge in multiuser transmissions. We present methods for constructing symbol-wise EP codes with the unique sum-pattern mapping (USPM) property using finite fields. Based on the orthogonal EP code constructed over GF($2^m$), we develop a time-division mode of finite-field multiple-access (FFMA) systems over a Gaussian multiple-access channel (GMAC), including both sparse-form and diagonal-form structures. Based on the diagonal-form (DF) structure, we introduce a specific configuration referred to as polarization-adjusted DF-FFMA, which achieves both power gain and coding gain across the entire blocklength. The proposed FFMA is then applied to network layer and forms network FFMA systems for pure digital networks. Simulation results demonstrate that, compared to popular complex-field MA systems, the proposed FFMA systems can offer superior error performance in a GMAC.

cs.IT↗