QC-LDPC Decoder Post-Processing for Trapping Set Error Floors
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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) or Sector Error Rate (SER), 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 set classes, allowing quasi-cyclic shifts to generate syndrome patterns of other class members and correct erroneous bits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If iterative decoding is used for QC-LDPC codes, then decoding complexity is reduced and computational efficiency is improved, but error floor performance deteriorates due to trapping sets that cannot be corrected
Solution Approach 1:
The decoding process is divided into two distinct stages: an iterative decoding stage that handles the majority of decoding tasks efficiently, and a post-processing stage that specifically addresses trapping set errors. This segmentation allows each stage to be optimized for its specific function, maintaining high computational efficiency while improving error floor performance.
Solution Approach 2:
The trapping set look-up table is pre-computed and stored before the actual decoding process. By pre-identifying and storing the characteristics of trapping sets, the decoder can quickly recognize and correct these problematic patterns during post-processing without performing complex real-time analysis, thus improving reliability without significantly increasing computational burden.
2Reliability
If a trapping set look-up table is added to correct trapping set errors, then error floor performance is improved, but device complexity increases due to additional processing stages and memory requirements
Solution Approach 1:
The trapping set look-up table is pre-computed and stored before the actual decoding process. By pre-identifying and storing the characteristics of trapping sets, the decoder can quickly recognize and correct these problematic patterns during post-processing without performing complex real-time analysis, thus improving reliability without significantly increasing computational burden.
Solution Approach 2:
Instead of implementing complex real-time trapping set detection and correction logic, the patent uses a pre-computed look-up table that stores the error patterns and correction information for known trapping sets. This copying approach replaces complex processing logic with simple table lookup and comparison operations, reducing device complexity while maintaining improved error floor performance.
3Measurement precision
If the look-up table stores syndrome patterns for all possible trapping sets, then trapping set identification accuracy is improved, but memory requirements and table size increase significantly
Solution Approach 1:
The look-up table stores detailed syndrome pattern information only for the most commonly occurring and problematic trapping sets, rather than all possible trapping sets. By focusing resources on the most critical cases, the patent achieves high identification accuracy for the trapping sets that matter most, while keeping the table size manageable.
Solution Approach 2:
The patent optimizes the look-up table by storing condensed representations of trapping set characteristics, such as syndrome weights and key identifying features, rather than complete syndrome patterns for all possible trapping sets. This parameter optimization maintains sufficient identification accuracy while significantly reducing memory requirements.
Data Source
AI summary
A QC-LDPC decoding system employing a trapping set look-up table is provided. The QC-LDPC decoding system includes an iterative decoder that utilizes a message-passing algorithm to decode a received codeword. If the iterative decoder fails to produce a valid codeword, additional processing is performed to decode the received codeword. The additional processing includes the steps of computing the syndrome pattern of the received codeword, searching the look-up table for a trapping set class that is responsible for the iterative decoder's failure, retrieving from the look-up table a syndrome pattern and an error pattern of a member of the responsible trapping set class, and calculating the error pattern of the received codeword based on its syndrome pattern and the information retrieved from the look-up table. The received codeword is then corrected based on its error pattern.