  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.
