Memory Cell Group Mapping for Fractional Bit Storage Reliability
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Solution Overview
Problem
Existing methods for mapping between program states and data patterns in semiconductor memory, particularly in fractional bit per cell configurations, often lead to error multiplication and propagation, and require redundancy or code expansion, which decreases capacity and increases complexity.
Innovation Solution
The method involves programming a group of memory cells such that their combined program states map to a constellation point corresponding to a data pattern, using a polynomial expression to determine the mapping between program states and data patterns, thereby avoiding redundancy and error propagation, and allowing for efficient fractional bit per cell mapping without code expansion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If existing mapping methods are used in fractional bit per cell configurations, then memory capacity can be utilized, but error multiplication and propagation occur
Solution Approach 1:
The invention segments the data pattern into multiple symbols, where each symbol is mapped to a group of memory cells rather than individual cells. This segmentation approach allows the system to handle fractional bit per cell configurations while maintaining reliability by distributing errors across multiple cells and symbols, thereby preventing error multiplication and propagation.
2Reliability
If redundancy or code expansion is used to prevent errors, then reliability improves, but capacity decreases and complexity increases
Solution Approach 1:
The invention changes the mapping parameters by using polynomial expressions of order equal to the number of memory cells in a group. This parameter change enables the system to achieve error prevention without requiring traditional redundancy or code expansion, thereby maintaining memory capacity while improving reliability through a mathematically rigorous mapping approach.
3Reliability
If redundancy or code expansion is used to ensure accurate mapping, then reliability improves, but device complexity increases
Solution Approach 1:
The invention replaces complex mechanical or algorithmic error correction mechanisms with a mathematical polynomial-based mapping system. By substituting traditional error correction codes with polynomial expressions, the system achieves accurate mapping with reduced complexity, as the polynomial approach provides inherent error resistance without requiring additional correction layers.
4Ease of manufacture
If traditional mapping methods are used, then implementation is straightforward, but packing density decreases
Solution Approach 1:
The invention merges multiple memory cells into groups that collectively represent single symbols in the polynomial mapping system. This merging approach increases packing density by efficiently utilizing fractional bit per cell configurations, while the systematic polynomial-based method maintains implementation simplicity through a unified mapping framework that handles both the grouping and mapping operations in an integrated manner.
Data Source
AI summary
The present disclosure includes methods and apparatuses for mapping between program states and data patterns. One method includes: programming a group of G memory cells such that a combination of respective program states of the group maps to a constellation point corresponding to a received N unit data pattern, the group used to store N/G units of data per memory cell; wherein the constellation point is one of a number of constellation points of a constellation associated with mapping respective program state combinations of the group of memory cells to N unit data patterns; and wherein the constellation comprises a first mapping shell and a second mapping shell, the constellation points corresponding to the respective first and second mapping shells determined, at least partially, based on a polynomial expression of order equal to G.