LDPC Decoding with Limited-Precision Soft Information in Flash Memories

TL;DR

This paper explores optimizing LDPC decoding in Flash memories using limited-precision soft information from multiple cell reads, demonstrating that mutual information maximization improves error correction performance.

Contribution

It introduces a method to optimize reference voltages for LDPC decoding in Flash memories by maximizing mutual information, accounting for quantization effects on code performance.

Findings

Mutual information maximization improves LDPC decoding performance.

Optimized quantization reduces frame error rates compared to non-optimized methods.

Small increases in soft information precision significantly outperform BCH codes without soft info.

Abstract

This paper investigates the application of low-density parity-check (LDPC) codes to Flash memories. Multiple cell reads with distinct word-line voltages provide limited-precision soft information for the LDPC decoder. The values of the word-line voltages (also called reference voltages) are optimized by maximizing the mutual information (MI) between the input and output of the multiple-read channel. Constraining the maximum mutual-information (MMI) quantization to enforce a constant-ratio constraint provides a significant simplification with no noticeable loss in performance. Our simulation results suggest that for a well-designed LDPC code, the quantization that maximizes the mutual information will also minimize the frame error rate. However, care must be taken to design the code to perform well in the quantized channel. An LDPC code designed for a full-precision Gaussian channel may perform poorly in the quantized setting. Our LDPC code designs provide an example where quantization increases the importance of absorbing sets thus changing how the LDPC code should be optimized. Simulation results show that small increases in precision enable the LDPC code to significantly outperform a BCH code with comparable rate and block length (but without the benefit of the soft information) over a range of frame error rates.