Rate-Adaptive LDPC Coding With Flexible Column Weights
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Solution Overview
Problem
Existing error correction schemes in memory subsystems using rate-adaptive LDPC codes are limited by parity-check matrices with columns of weight 1, which restricts their decoding correction capability.
Innovation Solution
Implementing rate-adaptive LDPC codes with flexible column weights in the parity check matrices, allowing for stronger correction capabilities by storing additional parities in a separate section of the memory device, and using a code generator to construct encoding and decoding matrices that optimize column weight distribution for improved error correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If parity-check matrices with columns of weight 1 are used in rate-adaptive LDPC codes, then the decoding complexity is reduced, but the error correction capability is limited
Solution Approach 1:
The patent applies dynamics by making the column weights adaptable rather than fixed. The parity-check matrices are designed with flexible column weights that can be adjusted based on the desired error correction capability. This allows the system to dynamically optimize between decoding complexity and error correction performance by selecting appropriate column weight distributions for different operating conditions.
Solution Approach 2:
The patent changes the parameter of column weights in the parity-check matrices from fixed weight-1 to flexible variable weights. By modifying this key parameter, the system achieves improved error correction capability while managing decoding complexity through optimized weight distributions. The code generator constructs matrices with specific weight patterns that balance these competing requirements.
2Reliability
If additional parities are stored in a separate section of the memory device to improve correction capability, then the error correction strength is enhanced, but the memory access time increases
Solution Approach 1:
The patent segments the parity storage into different sections within the memory device. Additional parities are stored in a separate section that can be accessed independently. This segmentation allows the system to retrieve only the necessary parity information for error correction without requiring access to the entire memory space, thereby reducing the time penalty associated with storing parities separately.
Solution Approach 2:
The patent implements preliminary action by pre-organizing the parity sections in the memory device during the encoding phase. The code generator constructs the parity-check matrices and prepares the parity storage layout in advance, so that when error correction is needed, the additional parities are already positioned for efficient retrieval. This preliminary organization minimizes the access time overhead.
3Reliability
If flexible column weights are implemented in parity check matrices, then the error correction capability is improved, but the code construction complexity increases
Solution Approach 1:
The patent introduces a code generator as an intermediary component that handles the complex task of constructing parity-check matrices with flexible column weights. This intermediary translates the requirement for flexible weights into concrete matrix constructions with optimized patterns. By delegating the complex construction task to this specialized component, the overall system manages code construction complexity while achieving improved error correction capability.
Solution Approach 2:
The patent manages construction complexity by systematically varying the column weight parameters according to predefined optimization criteria. Rather than allowing arbitrary flexibility, the system changes parameters in a controlled manner, using weight distributions that have been optimized for error correction performance. This structured approach to parameter changes reduces the complexity of code construction while maintaining the benefits of flexible weights.
Data Source
AI summary
Methods and system for error correction based on rate adaptive LDPC codes with flexible column weights in the parity check matrices are described. Data is encoded according to a first encoding parity check matrix of a first Low Density Parity Check (LDPC) code to obtain a first codeword with first parities. The first codeword is encoded according to a second encoding parity check matrix of a second LDPC code to obtain second parities. The first codeword is received. Responsive to failure of error correction of the first codeword based on the first parities, the second parities are received. The first codeword is corrected based on the second parities and a decoding parity check matrix of a rate adaptive LDPC code that is constructed by vertically concatenating the second encoding parity check matrix and the first encoding parity check matrix and adding an all-zero sub-matrix to complete its dimensions.