LDPC Encoder Circuit Using Factored Parity-Check Recursion
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Solution Overview
Problem
Conventional Low Density Parity Check (LDPC) encoding techniques are inefficient in hardware implementation due to the need for storing inverse matrices, which is cumbersome for modern data word sizes, especially in high-speed data communications where computational efficiency is crucial.
Innovation Solution
The approach involves factoring the parity check matrix into a form where a single block column is cyclic, allowing the solution of parity bits through a recursion path, reducing the need for inverse matrix storage and enabling efficient derivation of remaining parity bits using a custom architecture with cyclic multiply units.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional LDPC encoding techniques are used, then error correction capability is provided, but hardware implementation complexity increases due to the need for storing inverse matrices
Solution Approach 1:
The parity check matrix H is segmented into sub-matrices, where the lower triangular portion is factored into LU decomposition form. This segmentation allows the encoding process to be divided into manageable steps that avoid computing and storing the full inverse matrix, thereby reducing hardware complexity while maintaining error correction capability.
Solution Approach 2:
The inverse of the lower triangular sub-matrix is pre-computed and stored in a compact form during system initialization. This preliminary action eliminates the need for real-time inverse matrix computation during encoding, significantly reducing hardware complexity and processing time while preserving the reliability of error correction.
2Reliability
If conventional LDPC encoding techniques are used, then error correction is achieved, but memory requirements increase due to storing inverse matrices
Solution Approach 1:
The parity check matrix is segmented into sub-matrices, and only the inverse of the lower triangular sub-matrix is stored in LU decomposed form. This segmentation dramatically reduces the memory footprint compared to storing the full inverse matrix, while still enabling accurate computation of parity bits for error correction.
Solution Approach 2:
The matrix representation is transformed from storing the full inverse matrix to storing the LU decomposed form of the lower triangular portion. This parameter change in the data structure reduces memory requirements from O(n²) to a more manageable size, while preserving the mathematical properties needed for error correction.
3Reliability
If conventional LDPC encoding techniques are used, then comprehensive error correction is provided, but computational efficiency decreases
Solution Approach 1:
The LU decomposition of the lower triangular sub-matrix is performed in advance and stored. During encoding operations, the pre-decomposed form allows for rapid computation of parity bits through simple forward and backward substitution, significantly improving computational efficiency compared to computing the full inverse matrix in real-time.
Solution Approach 2:
The encoding computation is segmented into operations on the LU decomposed sub-matrices rather than operations on the full inverse matrix. This segmentation reduces the computational complexity from O(n³) to O(n²) or better, enhancing productivity while maintaining comprehensive error correction capability.
Data Source
AI summary
Encoder circuitry for applying a low-density parity check (LDPC) code to information words is disclosed. The encoder circuitry takes advantage of a macro matrix arrangement of the LDPC parity check matrix in which the parity portion of the parity check matrix is arranged as a macro matrix in which all block columns but one define a recursion path. The parity check matrix is factored so that the last block column of the parity portion includes an invertible cyclic matrix as its entry in a selected block row, with all other parity portion columns in that selected block row being zero-valued, thus permitting solution of the parity bits for that block column from the information portion of the parity check matrix and the information word to be encoded. Solution of the other parity bits can then be readily performed, from the original (non-factored) parity portion of the parity check matrix, following the recursion path.