LDPC Matrix Encoding for High-Block SSD Error Correction
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Solution Overview
Problem
Current LDPC code construction methods are inadequate for handling higher block lengths in solid state drive (SSD) systems, requiring efficient encoding methods and simple coding structures to achieve robust error-correcting performance and scalable code rates.
Innovation Solution
The development of new LDPC matrices based on algebraic relations, specifically constructing matrices H as [A|B] without a generator matrix, where A and B are designed to facilitate on-the-fly encoding, ensuring full rank and absence of short cycles, and using special linear group and Galois field-based structures for error correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional LDPC code construction methods are used, then error correction capability is maintained, but encoding efficiency deteriorates and memory requirements increase for higher block lengths
Solution Approach 1:
The LDPC code is segmented into multiple blocks, where each block can be encoded independently. This segmentation allows the encoder to process data in smaller chunks rather than requiring memory for the entire block length, thus improving encoding efficiency while reducing memory requirements for higher block lengths.
Solution Approach 2:
The patent pre-computes and stores only the essential parity-check matrix structures and encoding parameters rather than the entire generator matrix. This preliminary action reduces memory requirements while maintaining the ability to efficiently encode higher block lengths by using the pre-computed structures.
2Quantity of substance
If larger block lengths are used to increase storage capacity, then storage capacity is improved, but encoding complexity increases
Solution Approach 1:
Large block lengths are divided into smaller manageable segments that can be encoded using simplified procedures. This segmentation maintains storage capacity while reducing the complexity of encoding operations by breaking down the large-scale problem into smaller, more tractable sub-problems.
Solution Approach 2:
The patent changes the parameter representation from full generator matrices to compact parity-check matrix structures and encoding parameters. This parameter change allows larger block lengths to be handled with reduced encoding complexity by using more efficient mathematical representations.
3Productivity
If conventional encoding schemes are used, then data integrity is maintained, but throughput is reduced due to interleaver requirements
Solution Approach 1:
The patent extracts and eliminates the interleaver component from the conventional encoding scheme. By taking out the interleaver, throughput is improved as the encoding pipeline can operate continuously without the buffering and reordering operations that interleavers require, while data integrity is maintained through the inherent error correction capabilities of the LDPC code structure.
Data Source
AI summary
Some embodiments of the invention are directed to systems and methods for an optimized and efficient encoding scheme that can accommodate higher block lengths of data. Some embodiments generally relate to: (1) coding structures for a new class of LDPC matrices based on algebraic relations, and (2) encoding method that achieves the R=1−k/n exact bound on code rate. In addition, in some embodiments, the coding structures efficiently create matrices with excellent error-correcting properties and are devoid of short cycles (leading to robust performance). The implementations of the coding structures are scalable over a range of code rates and block lengths.