For binary source transmission, this paper proposes an element-pair (EP) coding scheme for supporting sourced massive random access, which is used to solve the finite blocklength (FBL) of multiuser reliability transmission problem. In this paper, we first give the definition of an EP, which is used as a virtual resource. If the Cartesian product of $J$ distinct EPs satisfies the unique sum-pattern mapping (USPM) structural property, the $J$ distinct EPs can form an uniquely-decodable EP (UD-EP) code. Then, we introduce a type of orthogonal EP code $\Psi_{\rm o, B}$ constructed over an extension field GF($2^m$). Based on the proposed EP code, we present finite-field multiple-access (FFMA) systems, including both the sparse-form-based and diagonal-form-based forms. Simulation results show that, for the massive random access scenario, the error performance of the proposed FFMA systems over a Gaussian multiple-access channel can provide much better error performance than that of a slotted ALOHA system.

翻译：针对二进制信源传输，本文提出了一种元素对（EP）编码方案以支持有源大规模随机接入，用于解决多用户可靠传输的有限块长（FBL）问题。首先，本文给出了EP的定义，将其作为一种虚拟资源。若$J$个不同EP的笛卡尔积满足唯一和模式映射（USPM）结构性质，则这$J$个不同EP可构成唯一可解码EP（UD-EP）码。随后，我们引入一种基于扩展域GF($2^m$)构造的正交EP码$\Psi_{\rm o, B}$。基于所提出的EP码，本文提出了有限域多址接入（FFMA）系统，包括稀疏形式和对角线形式两种实现方式。仿真结果表明，在大规模随机接入场景下，所提出的FFMA系统在高斯多址接入信道上的错误性能显著优于时隙ALOHA系统。