Finite-Field Coding for Unsourced Multiple Access

Unsourced multiple access (UMA) is a promising technique for the Internet-of-Things systems with a large number of users. In this paper, we explore the good algebraic properties of finite fields and propose a non-binary coding scheme for the UMA. The scheme is based on the slotted structure and T-fold ALOHA, and each active user randomly selects one slot to transmit its message. Finite-field operations are performed for both the channel coding and the multiple access. Compared to binary-field operations, the finite-field sparse spreading and multiuser superposition lead to improved diversity and less interference on each channel use. In addition, the non-binary LDPC code boosts the performance under short/moderate code length. We derive the joint belief-propagation decoding algorithm for the concatenated finite-field factor graph, which is then verified by the extrinsic information transfer (EXIT) analysis. The numerical results in terms of energy-efficiency performance are provided, which clearly demonstrate the superiority to the existing schemes in the region with large user numbers. The proposed scheme has the potential to carry out larger-scale user connections, and the energy-efficiency performance can be further improved by optimizing the coding parameters.