LDPC Encoder Circuit Using Cyclic Parity Matrix 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 proposed solution involves factoring the parity check matrix into a form where a single block column is cyclic, allowing for efficient derivation of parity bits using a recursion path, reducing the need for storing inverse matrices and simplifying the encoding process, suitable for high data rate applications like wireless broadband communications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional LDPC encoding techniques are used, then error correction capability is provided, but hardware implementation efficiency deteriorates due to the need for storing inverse matrices
Solution Approach 1:
The parity check matrix H is segmented into submatrices, with the parity portion H_p further divided into block columns. This segmentation allows the encoding process to be broken down into manageable steps, where each block column can be processed independently using the recursion path, eliminating the need to store and compute full inverse matrices.
Solution Approach 2:
The parity check matrix is pre-arranged into a specific structure where the parity portion consists of block columns with at least one cyclic submatrix each. This preliminary arrangement creates a recursion path that enables efficient computation during encoding, avoiding the need for inverse matrix storage while maintaining error correction capability.
2Reliability
If conventional LDPC encoding techniques are used, then error detection and correction is achieved, but memory requirements increase due to storing inverse matrices
Solution Approach 1:
The need to store inverse matrices is extracted and eliminated from the system. Instead of storing H_p^{-1}, the patent uses the pre-arranged structure of H with cyclic submatrices to compute parity bits on-the-fly through recursion, significantly reducing memory requirements while maintaining error detection capability.
Solution Approach 2:
The patent changes the structural parameters of the parity check matrix by arranging H_p into block columns with cyclic submatrices. This parameter change transforms the encoding process from one requiring inverse matrix storage to one that uses simple cyclic operations, reducing memory requirements from O(n^2) to O(n).
3Reliability
If conventional LDPC encoding techniques are used, then comprehensive error correction is provided, but computational complexity increases making real-time encoding difficult
Solution Approach 1:
The encoding computation is segmented into operations on individual block columns of H_p. Each block column processing involves simple cyclic shifts and XOR operations rather than full matrix inversion, reducing computational complexity from O(n^3) to O(n) while maintaining comprehensive error correction through the systematic generation of all parity bits.
Solution Approach 2:
The cyclic nature of the submatrices introduces periodicity to the encoding process. Each cyclic submatrix can be processed using repeated shift operations, transforming complex matrix operations into simple periodic shifts and accumulations, thereby reducing computational complexity while preserving 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.