GLDPC Decoding with Permutation-Based Error Floor Correction
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Solution Overview
Problem
Generalized low-density parity-check (GLDPC) codes based on Hamming codes face an error floor issue, limiting their raw bit-error rate (rBER) coverage to moderate target frame error rates, which is insufficient for nonvolatile memories like NAND flash that require very low frame error rates.
Innovation Solution
A method involving an iterative decoder that identifies oscillating states, estimates visible and hidden error rows, and corrects data using permutation-based error correction to overcome the error floor in GLDPC codes for NAND flash memories.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If GLDPC codes based on Hamming codes are used for error correction, then encoding and decoding complexity is reduced, but error correction capability is insufficient for very low frame error rate requirements
Solution Approach 1:
The error correction process is segmented into multiple phases: initial decoding attempt, oscillation detection, visible error row identification, hidden error row detection through permutation, and iterative correction. This segmentation allows the system to handle different types of errors systematically without requiring overly complex encoding schemes.
Solution Approach 2:
The system performs preliminary actions by detecting decoder oscillation early in the process and identifying visible error rows before attempting to correct hidden errors. This preliminary identification of error patterns enables more efficient subsequent correction steps.
2Device complexity
If iterative decoding is applied to GLDPC codes, then decoding complexity remains low, but the decoder oscillates between states and fails to correct errors
Solution Approach 1:
The system implements feedback by monitoring the decoder's iteration process to detect oscillation between states. When oscillation is detected, the system feeds back this information to trigger alternative correction mechanisms, including visible error row identification and hidden error row detection through permutation operations.
Solution Approach 2:
The error correction approach dynamically adapts based on decoder behavior. The system transitions from standard iterative decoding to oscillation-aware correction strategies when needed, and further adapts by attempting different permutation operations to reveal hidden errors that prevent convergence.
3Ease of operation
If standard error correction is used, then decoding is simple, but hidden error rows cannot be detected and correction is incomplete
Solution Approach 1:
The system detects hidden error rows by transforming the problem into another dimension through permutation operations. By permuting columns of the parity check matrix and re-decoding, the system reveals errors that were invisible in the original configuration, effectively adding a dimensional transformation to the detection process.
Solution Approach 2:
Permutation operations serve as an intermediary mechanism between standard decoding and hidden error detection. The permutation transforms the data representation temporarily, allowing hidden errors to become visible, then maps the findings back to the original data structure for correction.
Data Source
AI summary
A method of correcting data stored in a memory device includes: applying an iterative decoder to the data; determining a total number of rows in first data the decoder attempted to correct; estimating first visible error rows among the total number that continue to have an error after the attempt; estimating residual error rows among the total number that no longer have an error after the attempt; determining second visible error rows in second data of the decoder that continue to have an error by permuting indices of the residual error rows according to a permutation; and correcting the first data using the first visible error rows.