Finite Field Multiple Access

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.