Union Bound Analysis for Spin-Torque Transfer Magnetic Random Access Memory (STT-MRAM) With Channel Quantization

TL;DR

A union bound analysis which can accurately predict the word error rates (WERs) of ECCs with maximum-likelihood (ML) decoding over the quantized STT-MRAM channel is proposed and results show that the proposed union-bound-optimized (UBO) quantizer can achieve better error rate performance than the state-of-art quantizers for STTs.

Abstract

As an emerging non-volatile memory (NVM) technology, spin-torque transfer magnetic random access memory (STT-MRAM) has received great attention in recent years since it combines the features of low switching energy, fast write/read speed, and high scalability. However, process variation and thermal fluctuation severely affect the data integrity of STT-MRAM, resulting in both write errors and read errors. Therefore, effective error correction codes (ECCs) are necessary for correcting memory cell errors. Meanwhile, the design of channel quantizer plays a critical role in supporting error correction coding for STT-MRAM. In this work, we propose a union bound analysis which can accurately predict the word error rates (WERs) of ECCs with maximum-likelihood (ML) decoding over the quantized STT-MRAM channel. The derived bound provides a theoretical tool for comparing the performance of ECCs with different quantization schemes at very low error rate levels without resorting to lengthy computer simulations. Moreover, we also propose a new criterion to design the channel quantizer by minimizing the WERs of ECC decoding that are obtained from the union bound analysis. Numerical results show that the proposed union-bound-optimized (UBO) quantizer can achieve better error rate performance than the state-of-art quantizers for STT-MRAM.

Figures (5)

• Figure 1: The structure of an STT-MRAM cell.
• Figure 2: ECC coded STT-MRAM system with channel quantization.
• Figure 3: Convergences speed of DE for the UBO quantizer with $q= 2$, $d_{min}=4$ and $A(d_{min})=8157$ at $\sigma_{0}/\mu_{0} = 9\%$ and $P_1= 1\times 10^{-5}$.
• Figure 4: Comparison between analytical and simulation WERs, with UBO quantizer with $q= 1,2,3$.
• Figure 5: Comparison between analytical and simulation WERs with different quantizers, for (a) $q= 2$; (b) $q= 3$ & $q\rightarrow \infty$.