Joint Optimization of Codeword Bit Distribution and Detection Threshold for Asymmetric STT-MRAM Channel

Asymmetric error characteristics in spin-transfer torque magnetic random-access memory (STT-MRAM), particularly the imbalance between logical '0' and '1' error probabilities, can significantly degrade system reliability under conventional modulation and error-correcting schemes. This issue is especially critical in sensor network applications, where STT-MRAM is widely adopted for its non-volatility, low standby power, and robustness under energy-constrained and intermittently active operation. Existing approaches typically optimize the detection threshold under the assumption of a fixed or equiprobable bit distribution, while sparse coding techniques impose a predefined imbalance without explicitly accounting for its interaction with threshold detection. In this paper, we formulate the bit error rate (BER) minimization problem as a joint optimization of the codeword bit distribution and the detection threshold over an asymmetric cascaded STT-MRAM channel. Analytical results reveal that the minimum BER is achieved when the error probabilities associated with transmitted '0' and '1' bits are balanced, which induces an intrinsic coupling between the optimal detection threshold and the codeword composition. Motivated by this insight, we propose a new family of threshold-matched probability codes (TMPCs), in which the proportion of logical '1's in each codeword is explicitly designed to match the optimal detection threshold of the underlying channel. The proposed coding framework generalizes conventional sparse modulation by enabling adjustable bit distributions while preserving low-complexity linear encoding and syndrome-based decoding. Numerical evaluations demonstrate that the TMPC achieves consistently lower BERs than existing sparse and fixed-distribution coding schemes across a wide range of STT-MRAM operating conditions, particularly under severe write asymmetry and resistance variation. These results indicate that the proposed joint design offers a principled and flexible approach for improving reliability in STT-MRAM-based sensor networks and non-volatile memory systems.