Nonlinear LLR Lookup Tables for LDPC Decoder Scaling
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Solution Overview
Problem
Hard disc drives using low-density parity-check (LDPC) codes for error correction face suboptimal performance due to scaling issues with log-likelihood ratios (LLRs) exchanged between detectors and decoders, as scaling values may not provide optimal performance for every LLR value.
Innovation Solution
Incorporating a non-linear look-up table (LUT) that maps first LLR values to second LLR values, allowing for optimized scaling between the detector and decoder, which can be time-dependent or specific to different regions of the storage medium, to enhance decoding performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If linear scaling values are used for LLR transformation, then the system complexity is low, but the decoding performance is suboptimal
Solution Approach 1:
The patent transforms the LLR values using a non-linear mapping function that changes the parameter transformation from linear to non-linear. This allows the system to adapt the scaling factor dynamically based on the input LLR magnitude, improving decoding performance by providing more accurate reliability information to the decoder while maintaining computational feasibility through pre-computed lookup tables.
Solution Approach 2:
The patent pre-computes and stores optimal non-linear mapping values in lookup tables before the actual decoding process. This preliminary action allows the system to achieve complex non-linear transformation performance without computing the transformations in real-time, thereby improving decoding accuracy while keeping the runtime computational complexity low.
2Measurement precision
If a non-linear LUT is used to optimize LLR scaling, then decoding accuracy is improved, but the device complexity increases
Solution Approach 1:
The patent uses lookup tables that store pre-computed non-linear mapping values, effectively creating a copy of the optimal transformation function. This allows the system to apply complex non-linear scaling without implementing the complex computation logic, as the pre-computed values are simply retrieved and applied during decoding operations.
3Productivity
If fixed scaling factors are applied to all LLR values, then the processing speed is high, but the sector failure rate increases
Solution Approach 1:
The patent applies different scaling factors to different ranges of LLR values through the non-linear mapping function. Small LLR values (low confidence) receive different scaling treatment than large LLR values (high confidence), allowing the system to optimize reliability for each region while maintaining overall processing efficiency through the use of lookup tables.
Data Source
AI summary
In one implementation, the disclosure provides a system including a detector configured to generate an output of a first log-likelihood ratio for each bit in an input data stream. The system also includes at least one look-up table providing a mapping of the first log-likelihood ratio to a second log-likelihood ratio. The mapping between the first log-likelihood ratio and the second log-likelihood ratio is non-linear. The system also includes a decoder configured to generate an output data stream using the second log-likelihood ratio to generate a value for each bit in the input data stream.