As modern data-centric applications such as neural inference and sensor-edge analytics expand, they increasingly encounter the von Neumann memory wall, suffering from excessive data movement overhead and stringent energy constraints. In-Memory Computing (IMC) utilizing emerging non-volatile technologies, such as Magnetic Tunnel Junctions (MTJs), promises to mitigate these bottlenecks. However, conventional binary radix-based IMC architectures suffer from excessive vulnerability to process-induced variations, restricted operating margins, and thermal noise. To bridge the gap between energy efficiency and computational reliability, this work proposes FALCON, a fault-tolerant, MTJ-based in-memory arithmetic architecture integrated with Stochastic Computing (SC). By encoding numerical values into uniform bit-streams, SC naturally absorbs localized soft errors and enables the execution of an essential suite of arithmetic operations using highly compact logic primitives directly within the memory arrays. FALCON integrates a deterministic bit mapping mechanism with reconfigurable logic-in-memory (LIM) structures, eliminating the need to transfer data to external processors or area- and power-hungry random number generators. Experimental results using 14 nm FinFET technology validate the correct functionality of FALCON even under aggressive voltage scaling, severe process variation, and noise injection levels up to 30%, making it a robust framework for reliability-critical edge AI applications. We investigate the proper functionality of FALCON on morphological closing as a realistic noise-tolerant image processing case study.

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