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As applications of Internet-of-things (IoT) rapidly expand, unscheduled multiple user access with low latency and low cost communication is attracting growing more interests. To recover the multiple uplink signals without strict access control under dynamic co-channel interference environment, the problem of blind demixing emerges as an important obstacle for us to overcome. Without channel state information, successful blind demixing can recover multiple user signals more effectively by leveraging prior information on signal characteristics such as constellations and distribution. This work studies how forward error correction (FEC) codes in Galois Field can generate more effective blind demixing algorithms. We propose a constrained Wirtinger flow algorithm by defining a valid signal set based on FEC codewords. Specifically, targeting the popular polar codes for FEC of short IoT packets, we introduce signal projections within iterations of Wirtinger Flow based on FEC code information. Simulation results demonstrate stronger robustness of the proposed algorithm against noise and practical obstacles and also faster convergence rate compared to regular Wirtinger flow algorithm. 

This work develops a novel design of joint detection and decoding receiver for multiple-input multiple output (MIMO) wireless transmissions that utilizes polar codes in forward error correction (FEC). To optimize the overall receiver performance, we integrate the polar code constraints during signal detection by relaxing and transforming FEC code constraints from the original Galois field to the real field. We propose a novel joint linear programming (LP) optimization formulation that takes into consideration the transformed polar code constraints when designing a novel receiver robust against practical obstacles including channel state information (CSI) errors, additive noises, co-channel interferences, and pilot contamination. Our newly proposed joint LP formulation can also be integrated with reduced complexity polar decoders such as successive cancellation (SC) and successive cancellation list (SCL) decoders to deliver superior receiver performance at low cost.