LDPC Parity Check Matrix Encoding With Greedy Triangularization
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Solution Overview
Problem
Conventional low-density parity check (LDPC) code techniques require complex coding operations and a large number of circuit components, making them unsuitable for certain devices or systems due to their resource-intensive nature.
Innovation Solution
The proposed solution involves generating codewords directly from a parity check matrix Hm, which is derived from the LDPC code, using a process called greedy upper triangularization, reducing the complexity and component requirements by eliminating the need for a traditional generator matrix Gm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional LDPC code techniques are used, then error correction capability is achieved, but device complexity and number of circuit components increase
Solution Approach 1:
The patent extracts and eliminates the traditional generator matrix Gm from the LDPC encoding process, retaining only the parity check matrix Hm. This extraction principle reduces the coding operation complexity by removing unnecessary computational steps while preserving the error correction capability through the simplified Hm-based encoding approach.
Solution Approach 2:
The patent uses the parity check matrix Hm to generate codewords directly, creating a simplified copy of the traditional encoding process that eliminates the need for generator matrix operations. This copying approach maintains the essential error correction function while reducing computational complexity.
2Reliability
If conventional LDPC code techniques are used, then error correction capability is achieved, but the number of circuit components increases
Solution Approach 1:
The patent extracts and removes the generator matrix Gm and its associated circuit components from the LDPC system, keeping only the parity check matrix Hm. This extraction directly reduces the quantity of circuit components required while maintaining error correction functionality through the streamlined Hm-based encoding process.
3Productivity
If traditional generator matrix Gm is used for encoding, then complete codeword generation is achieved, but encoding complexity increases
Solution Approach 1:
The patent extracts the essential encoding function from the traditional generator matrix approach and implements it directly through the parity check matrix Hm. This extraction eliminates the need for separate generator matrix operations, reducing encoding process complexity while maintaining productivity through the simplified direct encoding method.
Data Source
AI summary
Some embodiments include apparatus and methods for encoding message information. Such apparatus and methods can include using a parity check matrix of a low-density parity check (LDPC) code to generate a first matrix having an upper triangular sub-matrix. Parity information to encode the message information can be generated based on the first matrix if a total number of rows of the upper triangular sub-matrix is equal to the rank of the parity check matrix. If the total number of rows of the upper triangular sub-matrix is less than the rank of the parity check matrix, then a triangularization operation can be performed on a second sub-matrix of the first matrix to generate a second matrix. Parity information to encode the message information can be generated based on the second matrix. Other embodiments including additional apparatus and methods are described.