Polarized Element-Pair Code-Based FFMA Over a Gaussian Multiple-Access Channel

This paper presents polarized element-pair (EP) codes for polarization-adjusted finite-field multiple-access (PA-FFMA) systems. The core innovation of FFMA systems lies in exchanging the order of channel coding and multiplexing operations, making the superposition signals a structured codeword sharing the entire degrees of freedom (DoFs). In the FFMA framework, element-pairs (EPs) serve as virtual resources for user separation, where different EP codes provide distinct error performance characteristics. This paper proposes polarized EP codes for a massive-user FFMA system, indicating that the superposition signals are codewords of polar codes. We derive the channel capacity for this polarized EP code-based PA-FFMA system, then develop an optimal power allocation scheme to maximize the multiuser channel capacity. The code construction employs the Monte Carlo method for selecting the polarized index set. For decoding, we introduce two specialized algorithms: a successive cancellation list (SCL) decoder for the balanced information-parity section scenarios, and a top L bifurcated minimum distance (TopL -BMD) decoder for small payload cases. Simulations show that FFMA with SCL achieves about 0.7 dB gain at BER=10-5 with 7 users over Polar Spreading. As the user load increases, Polar Spreading is about 2 dB worse than uncoded BPSK at BER=10-5 with 18 users, while FFMA with TopL -BMD remains about 2.3 dB better than uncoded BPSK with 31 users. The proposed decoding algorithms also have lower complexity than the Polar Spreading system.