LDPC Parity Check Matrix Design to Prevent Erroneous Decoding
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Solution Overview
Problem
Low-density parity check (LDPC) codes have a short minimum distance between code words, leading to erroneous corrections and failure in accurately detecting errors in encoded data, which can result in incorrect decoding in systems like nonvolatile semiconductor memory and communication systems.
Innovation Solution
An error correction encoding and decoding apparatus that incorporates a linear encoder and LDPC encoder, using a parity check matrix that satisfies specific conditions to prevent erroneous corrections, combined with a CRC code for dual error detection, ensuring accurate error detection even in cases of LDPC decoder failures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LDPC code is used for error correction, then error correcting capability is improved, but minimum distance between code words becomes short leading to erroneous corrections
Solution Approach 1:
The patent segments the error correction system into two distinct parts: an inner LDPC code for primary error correction and an outer CRC code for error detection. This segmentation allows each code to perform its specialized function - LDPC corrects errors while CRC detects erroneous corrections, thereby resolving the contradiction between error correcting capability and minimum distance limitations.
Solution Approach 2:
The CRC code acts as an intermediary between the LDPC encoder and decoder. It provides an additional layer of verification that detects when LDPC has made erroneous corrections due to short minimum distance, allowing the system to identify and handle these cases appropriately.
2Reliability
If LDPC decoder is used, then error correction is performed, but erroneous corrections occur causing failure to accurately detect errors
Solution Approach 1:
The system implements feedback through the CRC check after LDPC decoding. The CRC validator provides feedback information about whether the decoded data is correct, allowing the system to detect erroneous corrections and request retransmission or apply alternative correction methods.
Solution Approach 2:
The CRC code is applied in advance as a preliminary check before final data acceptance. This preliminary action verifies the integrity of LDPC decoded data and prevents erroneous corrections from propagating through the system.
3Device complexity
If single error correction code is used, then decoding process is simple, but error detection rate is insufficient
Solution Approach 1:
The patent merges two error correction codes - LDPC and CRC - into a hybrid system. This combination allows the system to maintain the relatively simple LDPC decoding process while adding the CRC error detection capability, thereby improving error detection rate without excessively increasing complexity.
Data Source
AI summary
According to one embodiment, an error correction encoding apparatus includes a linear encoder and a low-density parity check (LDPC) encoder. The linear encoder supports a linear coding scheme enabling a parity check to be carried out by a division using a generating polynomial and applies the generating polynomial to input data to obtain linear coded data. The LDPC encoder applies a generator matrix corresponding to a parity check matrix for an LDPC code to the linear coded data to obtain output data. The parity check matrix satisfies Expression (1) shown in the specification.