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 the channel detector and decoder, as scaling values do not provide optimal performance for every LLR value.
Innovation Solution
A system incorporating non-linear look-up tables (LUTs) that map first LLR values to second LLR values, optimizing the scaling process between the detector and decoder, with the option for time-dependent selection of LUTs based on iterative decoding processes and channel characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If scaling values are used for LLR values exchanged between detector and decoder, then performance improvement is achieved, but optimal performance is not provided for every LLR value
Solution Approach 1:
The scaling function is segmented into multiple discrete scaling factors stored in look-up tables. Instead of using a single scaling value for all LLR values, the system divides the LLR range and assigns different scaling factors to different segments, allowing each segment to be optimized for its specific range of LLR values.
Solution Approach 2:
Different scaling factors are applied to different local ranges of LLR values. The look-up tables store scaling factors that are locally optimized for specific LLR ranges, ensuring that each local region of the LLR space receives the most appropriate scaling factor for its characteristics.
2Ease of manufacture
If linear scaling is used for LLR values, then implementation is simple, but decoding performance is suboptimal
Solution Approach 1:
The scaling parameter is changed from a single linear factor to multiple discrete scaling factors stored in look-up tables. The system transitions from a simple linear scaling model to a more complex multi-factor model that adapts the scaling parameter based on the specific LLR value range, thereby improving performance while maintaining reasonable implementation complexity through pre-computed tables.
3Reliability
If multiple look-up tables are used for different scaling factors, then optimal performance for different LLR values is achieved, but device complexity increases
Solution Approach 1:
The look-up table structure is designed to be universal and multi-functional. The same look-up table mechanism serves multiple purposes: storing scaling factors for different LLR ranges, providing adaptive scaling, and enabling performance optimization across various operating conditions. This universal structure reduces the need for separate complex mechanisms for each function.
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.