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 block length of multiuser reliability transmission problem. Each user is assigned to a unique EP and the collection of EPs assigned to the users has the unique sum-pattern mapping (USPM) structural property. In this paper, we first present methods for constructing two specific types of EP codes with USPM structural property based on finite fields, and their encoding. Based on the EP-coding, we propose finite-field MA (FFMA) systems, in which an EP is viewed as a virtual resource for MA communications. The proposed FFMA is then applied to network layer and forms network FFMA systems for pure digital networks. Simulation results show that the error performance of the proposed FFMA over a Gaussian multiple-access channel can approach the error performance as that of the single-user transmission.

翻译：在过去的几十年中，已开发并使用了多种多址接入通信技术。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，本文提出了一种基于元素对（EP）的编码方案，以支持大量用户进行短分组传输，解决了多用户有限块长可靠性传输问题。每个用户被分配一个唯一的EP，且分配给用户的EP集合具有唯一和模式映射（USPM）结构性质。本文首先基于有限域提出了两类具有USPM结构性质的EP码的构造方法及其编码方式。基于EP编码，我们提出了有限域多址接入（FFMA）系统，其中EP被视为多址接入通信的一种虚拟资源。随后，将所提出的FFMA应用于网络层，构建了纯数字网络的网络FFMA系统。仿真结果表明，所提出的FFMA在高斯多址接入信道上的错误性能可接近单用户传输的错误性能。