In the past several decades, various multiple-access (MA) techniques have been developed and used. These MA techniques are carried out in complex-field domain to separate the outputs of the users. It becomes problematic to find new resources from the physical world. It is desirable to find new resources, physical or virtual, to confront the fast development of MA systems. In this paper, an algebraic virtual resource is proposed to support multiuser transmission. For binary transmission systems, the algebraic virtual resource is based on assigning each user an element pair (EP) from a finite field GF($p^m$). The output bit from each user is mapped into an element in its assigned EP, called the output symbol. For a downlink MA system, the output symbols from the users are jointly multiplexed into a unique symbol in the same field GF($p^m$) for further physical-layer transmission. The EPs assigned to the users are said to form a multiuser algebraic uniquely decodable (UD) code. Using EPs over a finite field, a network, a downlink, and an uplink orthogonal/non-orthogonal MA systems are proposed, which are called finite-field MA (FFMA) systems. Methods for constructing algebraic UD codes for FFMA systems are presented. An FFMA system can be designed in conjunction with the classical complex-field MA techniques to provide more flexibility and varieties.

翻译：过去几十年间，各类多址接入技术不断发展并被广泛应用。这些多址技术均在复数域中实现用户输出信号的分离，然而从物理世界中寻找新资源正面临困境。为应对多址系统的高速发展，亟需发掘物理域或虚拟域的新资源。本文提出一种基于代数虚拟资源的多用户传输方案。针对二进制传输系统，该代数虚拟资源通过为每个用户分配有限域GF($p^m$)中的一个元素对来实现。每个用户的输出比特被映射为其分配元素对中的特定元素，称为输出符号。在下行多址系统中，各用户的输出符号被联合复用到同一有限域GF($p^m$)的唯一符号，以进行后续物理层传输。分配给用户的元素对构成多用户代数唯一可译码。通过有限域上的元素对，本文提出了网络、下行链路和上行链路的正交/非正交多址系统，统称为有限域多址接入系统。同时给出了有限域多址系统中代数唯一可译码的构造方法。该有限域多址接入系统可与经典复数域多址技术协同设计，以提供更强的灵活性和多样性。