Finite Field Multiple Access

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.