Magnetic random-access memory (MRAM) is a promising memory technology due to its high density, non-volatility, and high endurance. However, achieving high memory fidelity incurs high write-energy costs, which should be reduced for large-scale deployment of MRAMs. In this paper, we formulate a biconvex optimization problem to optimize write fidelity given energy and latency constraints. The basic idea is to allocate non-uniform write pulses depending on the importance of each bit position. The fidelity measure we consider is mean squared error (MSE), for which we optimize write pulses via alternating convex search (ACS). We derive analytic solutions and propose an alternating water-filling algorithm by casting the MRAM’s write operation as communication over parallel channels. Hence, the proposed alternating water-filling algorithm is computationally more efficient than the original ACS while their solutions are identical. Since the formulated biconvex problem is non-convex, both the original ACS and the proposed algorithm do not guarantee global optimality. However, the MSEs obtained by the proposed algorithm are comparable to the MSEs by complicated global nonlinear programming solvers. Furthermore, we prove that our algorithm can reduce the MSE exponentially with the number of bits per word. For an 8-bit accessed word, the proposed algorithm reduces the MSE by a factor of 21. We also evaluate MNIST dataset classification supposing that the model parameters of deep neural networks are stored in MRAMs. The numerical results show that the optimized write pulses can achieve 40% write-energy reduction for the same classification accuracy.

中文翻译：

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通过交替注水算法优化 MRAM 的写入保真度

磁性随机存取存储器 (MRAM) 因其高密度、非易失性和高耐用性而成为一种很有前途的存储技术。然而，实现高内存保真度会产生高写入能量成本，对于大规模部署 MRAM，应该降低成本。在本文中，我们制定了一个双凸优化问题，在给定能量和延迟约束的情况下优化写入保真度。基本思想是根据每个位位置的重要性分配不均匀的写入脉冲。我们考虑的保真度度量是均方误差 (MSE)，为此我们通过交替凸搜索 (ACS) 优化写入脉冲。我们推导出解析解并提出一个通过将 MRAM 的写操作转换为并行通道上的通信来交替注水算法。因此，所提出的交替注水算法在计算上比原始 ACS 更有效，而它们的解决方案是相同的。由于公式化的双凸问题是非凸的，原始 ACS 和所提出的算法都不能保证全局最优性。然而，通过所提出的算法获得的 MSE 与复杂的全局非线性规划求解器的 MSE 相当。此外，我们证明了我们的算法可以随着每个字的位数成倍地降低 MSE。对于 8 位访问字，所提出的算法将 MSE 降低了 21 倍。我们还评估了 MNIST 数据集分类，假设深度神经网络的模型参数存储在 MRAM 中。