Sparse Code With Minimum Hamming Distance of Three for Spin-Torque Transfer Magnetic Random Access Memory

Abstract

Spin-torque-transfer magnetic random access memory (STT-MRAM) has recently emerged as a promising technology to replace dynamic random access memory (DRAM). However, STT-MRAM faces challenges due to process variations and thermal fluctuations, resulting in independent errors during the writing and reading. The STT-MRAM systems employ encoder and decoder mechanisms to address these errors. In addition, to handle asymmetric write error probabilities, a sparse code approach was adopted. Here, we propose an innovative algorithm based on the Hamming code to encode a sparse code with a minimum Hamming distance (MHD) of three. Our encoder introduces a general method to directly generate sparse code with an MHD of three from the user data. Before multiplying the data vectors by the generator matrix, we preprocessed them using an inverse method to ensure that the output of the generator matrix remained sparse. Furthermore, by leveraging the sum-product and syndrome decoding algorithms, we designed decoders that complemented the encoder. The simulation results showed that our proposed model could improve the speed and performance of STT-MRAM devices while overcoming the complexity issue of previous studies.

Keywords

• Asymmetric write error rate
• cascaded channel
• error correction codes (ECCs)
• Hamming code
• non-volatile RAM
• sparse codes