Polar Code and Symbol Mapping Design for Multi-Level Cell Spin-Torque Transfer Magnetic Random Access Memory

Multi-level-cell (MLC) spin-torque transfer magnetic random access memory (STT-MRAM) suffers from reliability issues due to the highly asymmetric error rates of its hard and soft domains. In this communication, we have proposed to include a symbol mapper prior to writing bits to the MRAM and have jointly optimized the mapping and polar codes with iterative, soft-cancellation (SCAN) decoder. Specifically, we perform code search and symbol mapping based on the extrinsic information transfer curves of a posteriori probability demapper and the SCAN decoder. We identify a number of variations of Gray code-based mappings, each promising best waterfall, convergence, and/or error-floor performances. In particular, our simulation results demonstrate that one of our proposed mapping achieves a bit-error-rate which is nearly three orders of magnitude lower than that of the conventional binary mapping and outperforms other Gray-code variants at a resistance spread up to 18% and hard bit write errors up to multiples of 10⁻³.