LDPC Decoder Post-Processing Using Unsatisfied Checks
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Solution Overview
Problem
Low-density parity check (LDPC) codes often encounter error floors due to trapping sets or near-codeword failures, which hinder high-reliability data transmission and storage systems, as existing decoding techniques struggle to correct erroneous bits that form reinforcing cycles.
Innovation Solution
A post-processing system that modifies inputs or messages passed to the LDPC decoder to prevent convergence to trapping sets, by identifying unsatisfied checks and adjusting symbol positions or message values, allowing the decoder to re-evaluate the codeword and potentially produce a valid output.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If standard LDPC decoding is used, then decoding complexity is reduced, but error floor performance deteriorates due to trapping sets
Solution Approach 1:
The patent applies preliminary action by performing syndrome checking immediately after initial LDPC decoding to identify trapping sets before final output. The system checks whether the decoded codeword satisfies all parity check equations, and if not, detects the presence of trapping sets and triggers additional correction procedures. This preliminary detection mechanism prevents erroneous codewords with trapping sets from being output, thereby improving error floor performance without significantly increasing overall decoding complexity.
2Reliability
If additional decoding iterations are performed to correct trapping sets, then reliability improves, but decoding time increases
Solution Approach 1:
The patent implements feedback by using syndrome information from initial decoding to guide subsequent correction iterations. The syndrome calculator continuously provides feedback about which parity check equations are violated, allowing the decoder to focus correction efforts on specific trapping set locations rather than performing blind additional iterations. This feedback mechanism enables the system to achieve reliable error correction with minimal additional decoding time by targeting corrections only where needed.
3Reliability
If post-processing is applied to detect and correct trapping sets, then error floor performance improves, but device complexity increases
Solution Approach 1:
The patent applies the taking out principle by extracting and separately handling trapping set detection and correction as distinct post-processing steps. The syndrome checker extracts trapping set information from the decoded codeword, identifies specific error locations, and separates this detection function from the main decoding process. This extraction allows the system to apply targeted correction only to identified trapping sets rather than processing the entire codeword through complex post-processing, thereby improving error floor performance with moderate complexity increase.
Data Source
AI summary
Systems and methods are provided for decoding received codewords using an LDPC code. An LDPC post-processor is disclosed for performing post-processing when standard LDPC decoding fails due to a trapping set. The LDPC post-processor may direct the LDPC decoder to decode the received codeword again, but may change some of the inputs to the LDPC decoder so that the LDPC decoder does not fail in the same way. In one embodiment, the LDPC post-processor may modify the symbol positions in the received codeword that correspond to a particular unsatisfied check. In another embodiment, the LDPC post-processor may modify the messages in the decoder's iterative message algorithm that correspond to the symbol positions.