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We consider the usage of finite-length polar codes for the Gaussian multiple access channel (GMAC) with a finite number of users. Based on the interleave-division multiple-access (IDMA) concept, we implement an iterative detection and decoding non-orthogonal multiple access (NOMA) receiver that benefits from a low complexity, while scaling (almost) linearly with the amount of active users. We further show the conceptual simplicity of the belief propagation (BP)-based decoder in a step-by-step illustration of its construction. Beyond its conceptual simplicity, this approach benefits from an improved performance when compared to some recent work tackling the same problem, namely the setup of finite-length forward error-correction (FEC) codes for finite-number of users. We consider the 5<sup>th</sup> generation mobile communication (5G) polar code with a block length N= 512 applied to both a two-user and a four-user GMAC scenario with a sum-rate of R<inf>sum</inf> = 0.5 and R<inf>sum</inf> = 1, respectively. Simulation results show that a BP-based soft interference cancellation (SoIC) receiver outperforms a joint successive cancellation (JSC) scheme. Finally, we investigate the effect of a concatenated repetition code which suggests that alternative polar code design rules are required in multi-user scenarios.

Iterative Detection and Decoding of Finite-Length Polar Codes in Gaussian Multiple Access Channels