QC-LDPC Decoder Using Trapping Set Lookup for Error Floor Reduction
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Solution Overview
Problem
LDPC codes, particularly QC-LDPC codes, face an error floor issue in high SNR regions, where further improvements in channel conditions do not lead to lower Bit Error Rate (BER) due to the presence of trapping sets that iterative decoders cannot correct.
Innovation Solution
A decoder system is implemented with a primary iterative decoding stage followed by additional processing stages using a trapping set look-up table to identify and correct errors caused by trapping sets, which includes a syndrome pattern and error pattern for commonly occurring trapping sets, allowing quasi-cyclic shifts to generate syndrome patterns of other members within the same class.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If iterative decoding is used for QC-LDPC codes, then decoding speed and computational efficiency are improved, but error floor performance deteriorates due to trapping sets
Solution Approach 1:
The patent pre-calculates and stores syndrome patterns and corresponding error patterns for known trapping set classes in a look-up table before decoding operations. When decoding fails due to trapping sets, the system quickly retrieves pre-computed correction patterns from the table, avoiding the need for complex real-time analysis and enabling rapid error correction while maintaining high decoding speed
Solution Approach 2:
The patent introduces a look-up table as an intermediary component between the iterative decoder and the final decoded output. This table stores pre-computed syndrome-error pattern mappings for various trapping set classes, acting as a mediator that provides quick reference solutions when the iterative decoder encounters trapping sets, thereby improving reliability without significantly increasing computational complexity
2Reliability
If additional processing stages are added to correct trapping sets, then error floor performance is improved, but device complexity increases
Solution Approach 1:
The patent uses a look-up table that contains pre-stored syndrome patterns and corresponding error patterns for various trapping set classes. Instead of implementing complex real-time algorithms to identify and correct trapping sets, the system copies pre-computed correction patterns from the table based on syndrome pattern matching, significantly reducing the complexity of the additional processing stage while maintaining effective error floor reduction
Solution Approach 2:
The patent applies different decoding strategies to different types of errors: standard iterative decoding for general errors and look-up table-based correction specifically for trapping set errors. By localizing the complex correction mechanism to only when trapping sets are detected (identified through syndrome pattern matching), the system improves error floor performance while minimizing the increase in overall device complexity
3Reliability
If a comprehensive look-up table with all trapping set classes is stored, then error correction capability is improved, but memory requirements increase
Solution Approach 1:
The patent merges multiple trapping set classes into broader categories based on common characteristics, particularly focusing on short-cycle trapping sets that are most problematic. By grouping trapping sets with similar syndrome pattern structures and error correction requirements into unified classes, the system reduces the total number of entries needed in the look-up table while maintaining comprehensive error correction capability for the most critical trapping set types
Solution Approach 2:
The patent optimizes the representation of syndrome patterns and error patterns in the look-up table by using compact encoding schemes and focusing on the most significant parameters that distinguish different trapping set classes. By changing how the data is stored and represented (using optimized data structures and selective storage of critical patterns), the system reduces memory requirements while preserving the ability to identify and correct the most common and harmful trapping sets
Data Source
AI summary
A QC-LDPC decoding system employing a trapping set look-up table is provided. The entries of the trapping set look-up table may be sorted according to failure frequencies of the trapping sets. The decoder may determine short-cycles associated with dominant trapping sets in order to decode the received codeword. If the iterative decoder of the QC-LDPC decoding system fails to produce a valid codeword, the decoder may compute the syndrome pattern of the processed codeword and search the look-up table for a trapping set class that is responsible for the iterative decoder's failure. If no responsible trapping set is found in the look-up table, the decoder may attempt to decode the received codeword using alternate decoding methods and subsequently determine a trapping set associated with the decoded codeword. If a trapping set is determined, then that trapping set may be added to the look-up table.