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 proposes an element-pair (EP) coding scheme for supporting massive users with short packet traffic, which solves the finite blocklength (FBL) of multiuser reliability transmission problem. Each user is assigned a unique EP, and the collection of EPs assigned to the users possesses the unique sum-pattern mapping (USPM) structural property. We present methods for constructing symbol-wise EP codes with USPM structural property based on the prime field and extension field of prime field, respectively. Based on the orthogonal EP code constructed over GF($2^m$), we propose finite-field MA (FFMA) systems over a Gaussian multiple-access channel (GMAC), including both the sparse-form and diagonal-from structures. The proposed FFMA is then applied to network layer and forms network FFMA systems for pure digital networks, in which an EP is viewed as a virtual resource block (VRB). Simulation results show that the error performance of the proposed FFMA over a GMAC can approach the error performance as that of the single-user transmission.

翻译：在过去的几十年中，多种技术被开发并用于多址接入通信。随着6G新应用的出现，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，本文提出一种用于支持海量用户短包业务的元素对编码方案，该方案解决了多用户可靠性传输的有限块长问题。每个用户被分配一个唯一的元素对，而分配给用户的元素对集合具有唯一和模式映射结构特性。我们分别提出了基于素域及其扩域构建具有USPM结构特性的符号级EP码的方法。基于在GF($2^m$)上构建的正交EP码，我们提出了高斯多址接入信道上的有限域多址接入系统，包括稀疏形式和斜对角形式两种结构。所提出的FFMA随后被应用于网络层，形成面向纯数字网络的网络FFMA系统，其中EP被视为虚拟资源块。仿真结果表明，所提出的GMAC上FFMA系统的误码性能可逼近单用户传输的误码性能。