Sparse Code With Minimum Hamming Distances of 4 and 5 for Increasing the Density of STT-MRAM Cells

With the development of flash memory, the spin-transfer torque magnetic random access memory (STT-MRAM) is considered as a promising technology for broader applications due to its nonvolatility, fast access, and high density. In STT-MRAM, digital data are converted into resistance values, which are then read by the current passing through the magnetic tunnel junction (MTJ) in STT-MRAM. However, this current is affected by temperature, leading to resistance offsets. Additionally, process variations create unpredictable effects. These factors cause random and asymmetric errors in STT-MRAM. To address these issues, previous studies proposed sparse codes with a minimum Hamming distance (MHD) of 3. These codewords are based on the Hamming codes, which ensure an MHD of 3. Inspired by this, to maintain the bit error rate (BER) performance with a high-density STT-MRAM array, we propose a method to generate a generator matrix that can increase the MHD to 4 and 5, which is not available with Hamming codes. We analyzed binary sequences to create criteria for the parity matrix. Finally, these parity matrices are combined with the unit matrix to create the generator matrix. Using the generator matrix, we created sparse codes with MHDs of 4 and 5. These sparse codewords were then applied to the STT-MRAM array. Simulation results showed that our proposed model could improve the performance of STT-MRAM devices as the cell density increases.