QC-LDPC Encoding Using Sparse Parity-Check Matrix Blocks
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Solution Overview
Problem
Conventional LDPC code encoding methods result in large computational costs due to the high number of non-zero elements in the matrices used, leading to increased circuit scale and complexity.
Innovation Solution
The proposed error correction encoding method divides the encoding process into two steps: sparse matrix computation and matrix multiplication, using a sparse parity-check matrix and an inverse matrix to reduce the size of the matrices involved, thereby minimizing the number of exclusive OR operations and circuit complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a lower triangular matrix is used for encoding, then encoding can be performed by backward substitution, but the number of non-zero elements increases and the amount of computations increases
Solution Approach 1:
The parity-check matrix H is segmented into submatrices with specific structures (circulant permutation matrices and zero matrices). This segmentation allows the encoding process to exploit the sparse structure and perform computations more efficiently without requiring conversion to a full lower triangular matrix, thus reducing the number of non-zero elements and computational operations.
Solution Approach 2:
The invention changes the parameter representation by using circulant permutation matrices with shift parameters instead of dense lower triangular matrices. By representing the matrix in terms of circulation shifts rather than explicit non-zero elements, the computational complexity is reduced while maintaining the ability to perform encoding operations.
2Ease of operation
If the parity-check matrix is converted to a lower triangular matrix, then encoding can be performed, but the sparse structure is lost and the number of non-zero elements increases
Solution Approach 1:
The matrix is segmented into blocks where most blocks are zero matrices and only specific blocks contain circulant permutation matrices. This block segmentation preserves the sparse structure by maintaining large zero regions while enabling systematic encoding through the non-zero block patterns.
Solution Approach 2:
Instead of converting the sparse parity-check matrix to a dense lower triangular matrix (the conventional approach), the invention inverts the approach by directly using the sparse structured matrix with circulant permutation matrices for encoding. This reversal avoids the transformation that would increase non-zero elements while still enabling encoding operations.
3Productivity
If a generator matrix with many 1s is used, then the parity bit sequence can be determined, but the number of exclusive OR operations increases and the amount of computations increases
Solution Approach 1:
The invention changes the computational parameters by using circulant permutation matrices with shift operations instead of generator matrices with many 1s. The encoding operation transforms from multiple exclusive OR operations to a smaller number of cyclic shift operations and additions, significantly reducing the computational count while maintaining encoding productivity.
Data Source
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AI summary
An error correction encoding device 1 includes a sparse matrix computing unit 2 that computes exclusive OR of a submatrix, in a parity-check matrix, corresponding to an information bit sequence, and the information bit sequence on the basis of the position of 1 in the submatrix to calculate a vector, a fundamental matrix operator 3 that calculates a predetermined matrix by performing a predetermined fundamental matrix operation on a submatrix, in the parity-check matrix, corresponding to a parity bit sequence, and a matrix multiplier 4 that calculates the parity bit sequence by multiplying the predetermined matrix which the fundamental matrix operator 3 calculates, and the vector which the sparse matrix computing unit 2 calculates.