Maximum Achievable Rate of Resistive Random-Access Memory Channels by Mutual Information Spectrum Analysis

TL;DR

Maximum achievable rates of the ReRAM channel with different settings, such as single- and across-array codings, with and without data shaping, and optimal and treating-interference-as-noise (TIN) decodings, are compared and provide valuable insights on the code design for ReRAM.

Abstract

The maximum achievable rate is derived for resistive random-access memory (ReRAM) channel with sneak path interference. Based on the mutual information spectrum analysis, the maximum achievable rate of ReRAM channel with independent and identically distributed (i.i.d.) binary inputs is derived as an explicit function of channel parameters such as the distribution of cell selector failures and channel noise level. Due to the randomness of cell selector failures, the ReRAM channel demonstrates multi-status characteristic. For each status, it is shown that as the array size is large, the fraction of cells affected by sneak paths approaches a constant value. Therefore, the mutual information spectrum of the ReRAM channel is formulated as a mixture of multiple stationary channels. Maximum achievable rates of the ReRAM channel with different settings, such as single- and across-array codings, with and without data shaping, and optimal and treating-interference-as-noise (TIN) decodings, are compared. These results provide valuable insights on the code design for ReRAM.

Figures (5)

• Figure 1: Sneak path during the reading of cell $(3, 2)$ in a $4\times 4$ memory array. (a) is the memory array and (b) is the corresponding data array. The green line is the desired current path for resistance measuring and the red line going through cells $(3, 2)\rightarrow(3, 4)\rightarrow(1, 4) \rightarrow(1, 2)\rightarrow(3, 2)$ is a sneak path. Note that word lines and bit lines are connected via memory cells. Arrows show current flow directions. A reverse current flows across cell $(1, 4)$.
• Figure 2: A memory array with SF pattern $\varphi=\{(i_1,j_1), (i_2, j_2)\}$. The readback signal $R_{x_{m,n}}\left((x_{m,j_1}x_{i_1,j_1}x_{i_1,n})\bigcup (x_{m,j_2}x_{i_2,j_2}x_{i_2,n})\right)$ of cell $(m,n)$ (without noise) is determined by data stored at the cell $x_{m,n}$, data at the SF locations $x_{i_1,j_1}, x_{i_2,j_2}$, and data in the SF rows and columns $x_{i_1,n}, x_{i_2,n}$ and $x_{m,j_1}, x_{m,j_2}$.
• Figure 3: Mutual information spectrum of ReRAM channel with $q=0.5$, $R_1=100\ \Omega, R_0=1000\ \Omega, R_s=250\ \Omega, \sigma=50$. SF number is with $\mathcal{B}_K(n,\mu)$ with $n=256\times 256, \mu=10^{-4}, K=8$.
• Figure 4: Spectral inf-mutual information rate of ReRAM channel for both single- and across-array codings with varying $q$. $R_1=100\ \Omega, R_0=1000 \Omega, R_s=250\ \Omega, K=8$.
• Figure 5: Maximum achievable rate $\mathcal{R}$ of ReRAM channel under both of the optimal and TIN decodings. $R_1=100\ \Omega, R_0=1000\ \Omega, R_s=250 \Omega, K=8$.

Theorems & Definitions (14)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Example 1: $\Phi=\phi$
• Theorem 1: Mutual Information Spectrum
• Theorem 2: Single-Array Coding Rate
• Theorem 3: Across-Array Coding Rate
• Lemma 1