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, effectively addressing the finite blocklength (FBL) challenge in multiuser transmission.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.

翻译：过去数十年间，多种技术被开发并应用于多址接入通信。随着6G新应用场景的出现，亟需寻找新的物理或虚拟资源以应对多址接入通信系统的快速发展。针对二进制信源传输，本文引入元素对概念，通过$J$个相异元素对的笛卡尔积可构成元素对码。元素对被视为有限域中的虚拟资源以区分用户。该方法允许重新编排信道编码与复用模块，有效应对多用户传输中的有限码长挑战。我们提出了利用有限域构建具有唯一和模式映射特性的符号级元素对码的方法。基于GF($2^m$)上构建的正交元素对码，我们开发了高斯多址信道上有限域多址接入系统的时分模式，包括稀疏形式与对角形式两种结构。基于对角形式结构，我们引入了一种特定配置——极化调整对角形式有限域多址接入，该配置能在整个码长范围内同时实现功率增益与编码增益。所提出的有限域多址接入技术进一步应用于网络层，构建了面向纯数字网络的网络有限域多址接入系统。仿真结果表明，相较于当前主流的复数域多址接入系统，所提出的有限域多址接入系统在高斯多址信道上能提供更优异的误码性能。