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 by signal processing which consumes physical resources to separate the outputs of the users. It becomes problematic to find new resources from the physical world. In this paper, an algebraic resource is proposed to support multiuser transmission. This algebraic 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. Then, the output symbols from the users are jointly mapped into a unique symbol in the same field GF($p^m$) for modulation and transmission. The EPs assigned to the users are said to form a set of uniquely decodable EPs (UDEPs), called a multiuser UD code. Using UDEPs over a finite field, a downlink and an uplink MA systems are proposed, which are called finite-field MA (FFMA) systems. Methods for constructing finite-field UD codes for FFMA systems are provided. An FFMA system can be designed in conjunction with the classical complex-field MA techniques to provide more flexibility and varieties.

翻译：在过去的几十年中，各种多址接入技术已被开发并得到应用。这些多址技术通过在复数域进行信号处理来实现，其消耗物理资源以分离不同用户的输出信号。从物理世界中寻找新资源已变得困难。本文提出一种代数资源以支持多用户传输。该代数资源基于将有限域GF($p^m$)中的元素对分配给每个用户。每个用户输出的比特被映射到其分配元素对中的一个元素，称为输出符号。随后，所有用户的输出符号被联合映射到同一有限域GF($p^m$)中的唯一符号，用于调制和传输。分配给用户的元素对被定义为构成一组唯一可解码元素对，称为多用户UD码。利用有限域上的UDEP，本文提出了下行链路和上行链路多址系统，称为有限域多址系统。本文还提供了用于FFMA系统的有限域UD码的构造方法。FFMA系统可与经典复数域多址技术联合设计，以提供更强的灵活性和多样性。