Interleaved Multi-Dimensional Encoding for Low Error-Floor NAND Flash
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Solution Overview
Problem
Existing multi-dimensional encoding methods in NAND flash memory systems face challenges in achieving a low error-floor and efficient operation, particularly in maintaining an extremely low output bit error rate (BER) below ten to the power of minus fifteen, due to limitations in protecting the redundancy of one dimension without involving it in the encoding process.
Innovation Solution
The proposed solution involves an interleaved multi-dimensional encoding scheme where encoding results of one dimension affect and are affected by those of another dimension, allowing for joint redundancy across multiple dimensions, enabling efficient protection and calculation of codeword components without relying solely on additional codes for redundancy protection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional multi-dimensional encoding methods are used, then the encoding process is simpler and does not involve joint redundancy, but the error-floor remains high and the output bit error rate cannot achieve below ten to the power of minus fifteen
Solution Approach 1:
The patent merges the encoding processes of multiple dimensions by calculating codeword components of different dimensions in an interleaved manner. Specifically, when calculating codeword components for the first dimension, the method incorporates redundancy information from the second dimension, and vice versa. This merging allows joint redundancy to be generated, where the redundancy of one dimension protects not only its own data but also the redundancy of other dimensions, thereby achieving the required bit error rate below 10^-15 while maintaining encoding efficiency.
Solution Approach 2:
The patent extends traditional single-dimension encoding to multi-dimensional encoding by introducing additional dimensions for data organization. The method arranges data bits in a multi-dimensional structure and performs encoding operations across multiple dimensions, where each dimension contributes to the overall redundancy protection. This dimensional extension enables the system to achieve the required reliability by distributing and protecting redundancy across multiple dimensions rather than relying on a single encoding pass.
2Reliability
If redundancy of one dimension is protected without involving it in the encoding process, then the encoding process is faster and more efficient, but the error-floor cannot be reduced sufficiently
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing redundancy information from one dimension before performing the encoding of another dimension. Specifically, when calculating codeword components for the first dimension, the method uses pre-computed redundancy from the second dimension as input. This preliminary preparation of redundancy information allows the encoding process to achieve low error-floor without requiring additional encoding passes, thereby maintaining encoding efficiency while significantly reducing the error-floor.
Solution Approach 2:
The patent implements feedback mechanisms where the redundancy information generated from encoding one dimension is fed back into the encoding process of other dimensions. The method calculates codeword components of the first version using redundancy of data entities from the second version, and vice versa. This feedback loop ensures that redundancy is effectively utilized across dimensions, reducing the error-floor while avoiding the need for separate protection processes that would reduce encoding efficiency.
3Reliability
If joint redundancy is implemented across multiple dimensions, then the error-floor is reduced and reliability is improved, but the encoding process becomes more complex and computationally intensive
Solution Approach 1:
The patent segments the encoding process into distinct stages and dimensions, where each dimension is encoded separately but with interleaved redundancy calculation. The method divides the data into multiple versions (first version, second version, etc.) corresponding to different dimensions, and processes each dimension's codeword components in a structured sequence. This segmentation allows the complex joint redundancy operation to be broken down into manageable steps, reducing implementation complexity while maintaining the reliability benefits of multi-dimensional joint encoding.
Solution Approach 2:
The patent applies local quality by allowing different codeword components to have different properties based on their position and dimension. Specifically, the method calculates a majority of codeword components of the first version in response to data entities of the second version, while calculating a minority of codeword components regardless of the second version. This localized differentiation optimizes the encoding process by applying joint redundancy only where necessary, reducing overall computational complexity while maintaining error-floor performance.
Data Source
AI summary
A method for interleaved multi-dimensional encoding, the method may include receiving or generating a first version of a group of bits and a second version of the group of bits, wherein the first and second versions differ from each other by an arrangement of bits of the group of bits; and encoding the first and second versions of the groups of bits in an interleaved manner; wherein the encoding comprises calculating at least one codeword component of the first version by encoding a set of bits of the first version and at least a portion of a redundancy of at least one data entity of the second version and calculating at least one codeword component of the second version by encoding a set of bits of the second version and at least a portion of a redundancy of at least one data entity of the first version.