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Performance Analysis and Code Design for Resistive Random-Access Memory Using Channel Decomposition Approach

Guanghui Song, Meiru Gao, Ying Li, Bin Dai, Kui Cai

TL;DR

This work tackles the sneak-path problem in ReRAM by modeling the non-ergodic, data-dependent channel as a mixture of stationary $\lambda$-Gaussian channels and deriving a finite-length performance bound from capacity and dispersion. It then develops a two-dimensional density-evolution framework to design practical sparse-graph codes (e.g.,IRA codes) optimized for the decomposed channel, achieving decoding thresholds close to the bound. The key contributions are (i) a rigorous channel-decomposition method with a $F_N(\lambda)$ SP-rate distribution, (ii) closed-form approximations for $C_{\lambda}$ and $V_{\lambda}$ enabling tractable finite-length analysis, and (iii) a low-complexity DE-based code-design pipeline validated by simulations that link original ReRAM performance to the decomposed-channel predictions.

Abstract

A novel framework for performance analysis and code design is proposed to address the sneak path (SP) problem in resistive random-access memory (ReRAM) arrays. The main idea is to decompose the ReRAM channel, which is both non-ergodic and data-dependent, into multiple stationary memoryless channels. A finite-length performance bound is derived by analyzing the capacity and dispersion of these stationary memoryless channels. Furthermore, leveraging this channel decomposition, a practical sparse-graph code design is proposed using density evolution. The obtained channel codes are not only asymptotic capacity approaching but also close to the derived finite-length performance bound.

Performance Analysis and Code Design for Resistive Random-Access Memory Using Channel Decomposition Approach

TL;DR

This work tackles the sneak-path problem in ReRAM by modeling the non-ergodic, data-dependent channel as a mixture of stationary -Gaussian channels and deriving a finite-length performance bound from capacity and dispersion. It then develops a two-dimensional density-evolution framework to design practical sparse-graph codes (e.g.,IRA codes) optimized for the decomposed channel, achieving decoding thresholds close to the bound. The key contributions are (i) a rigorous channel-decomposition method with a SP-rate distribution, (ii) closed-form approximations for and enabling tractable finite-length analysis, and (iii) a low-complexity DE-based code-design pipeline validated by simulations that link original ReRAM performance to the decomposed-channel predictions.

Abstract

A novel framework for performance analysis and code design is proposed to address the sneak path (SP) problem in resistive random-access memory (ReRAM) arrays. The main idea is to decompose the ReRAM channel, which is both non-ergodic and data-dependent, into multiple stationary memoryless channels. A finite-length performance bound is derived by analyzing the capacity and dispersion of these stationary memoryless channels. Furthermore, leveraging this channel decomposition, a practical sparse-graph code design is proposed using density evolution. The obtained channel codes are not only asymptotic capacity approaching but also close to the derived finite-length performance bound.

Paper Structure

This paper contains 24 sections, 73 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Coded ReRAM System Model
  3. Channel Decomposition and Finite-Length Analysis
  4. Probability Distribution of SP Rate $F_N(\lambda)$
  5. $E[\lambda_N]$
  6. $D[\lambda]$
  7. Gaussian Approximation of $F_N(\lambda)$
  8. Channel Capacity and Dispersion of $\lambda$-Gaussian Channel
  9. Channel Capacity $C_\lambda$
  10. Channel Dispersion $V_{\lambda}$
  11. Density Evolution and Iterative Decoding Threshold Over $\lambda$-Gaussian Channel
  12. Gaussian Approximation of LLR
  13. HRS Cell
  14. LRS Cell
  15. SP Cell
  16. ...and 9 more sections

Figures (12)

  • Figure 1: (a) A $4\times4$ ReRAM array and (b) The corresponding data array. The green line plots the desired path when measuring the resistance of cell $(3, 2)$, and the red line forms an SP. Arrows show current flow directions. A reverse current flows across cell $(1, 4)$.
  • Figure 2: PDF of the detected resistance value $y_{m,n}$ when the cell is an LRS cell ($x_{m,n}=1$), a HRS cell ($x_{m,n}=0$ without SP interference), or an SP cell ($x_{m,n}=0$ with SP interference). The associated resistance values are $R_0=1000\ \Omega, R_1=100\ \Omega$, and $R_s=250\ \Omega$, and the noise standard deviation is $\sigma=30$.
  • Figure 3: System model of Coded ReRAM.
  • Figure 4: $\lambda$-Gaussian channel model.
  • Figure 5: An example of scattered and non-scattered SF patterns.
  • ...and 7 more figures