Quasi-Cyclic LDPC Code Structure for Low-Complexity Error Correction
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Solution Overview
Problem
Existing data transmission technologies face challenges in efficiently correcting errors over noisy media using low-density parity check codes, particularly due to the complexity of implementing parity matrices with Hamming weights greater than 2, which restricts the features of these codes and increases implementation costs.
Innovation Solution
The introduction of a quasi-cyclic low-density parity check code (QC-LDPC) with a triple diagonal structure in the parity matrix Hb1, allowing for a lower number of columns with a Hamming weight less than or equal to 2, while maintaining negligible complexity increase, thereby enhancing error correction capabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a parity matrix with Hamming weight greater than 2 is used, then error correction capability is improved, but implementation complexity increases
Solution Approach 1:
The parity matrix H is segmented into submatrices H1, H2, H3 with specific structures. H1 contains the information bits, H2 contains the parity bits, and H3 is a structured matrix with specific diagonal patterns. This segmentation allows the matrix to achieve high error correction capability through its structured design while keeping implementation complexity manageable through the regular patterns in each submatrix.
Solution Approach 2:
The invention changes the structural parameters of the parity matrix by introducing a specific form with diagonal patterns and controlled Hamming weights. By parameterizing the matrix structure with specific diagonal elements and zero patterns, the invention achieves both high reliability (through proper Hamming weight distribution) and controlled complexity (through the regular parametric structure that can be efficiently implemented).
2Device complexity
If a structured parity matrix is used, then implementation complexity is reduced, but error correction features are restricted
Solution Approach 1:
The invention introduces dynamics by allowing the diagonal elements of submatrix H3 to be non-zero values that can be adjusted based on the specific application requirements. This dynamic parameter adjustment enables the structured matrix to adapt to different error correction needs while maintaining the overall structured form, thus achieving both low complexity and high error correction capability.
Solution Approach 2:
The parity matrix is constructed as a composite structure combining multiple submatrices (H1, H2, H3) with different functions. H1 provides the information bit storage, H2 provides the parity bit generation, and H3 provides the structured error correction capability. This composite structure allows each submatrix to be optimized for its specific function while working together to achieve both low complexity and high error correction features.
Data Source
AI summary
A method including selecting a factor based on a number of bits in a codeword and a natural number and generating a model matrix including first and second matrices having data and parity bits. Hamming weights of the model matrix are not constant and Hamming weights of columns of the model matrix follow a statistical distribution dependent upon a codification rate of a channel. A compact matrix is generated by replacing elements of the model matrix equal to: 1 with a pseudo-random positive whole number; and 0 with −1. A quasi-cyclic code is generated by replacing in the compact matrix: positive elements with identity matrices; and elements equal to −1 with null matrices. A number of rows and columns in each of the identity and null matrices is equal to the factor. The quasi-cyclic code is applied to a word to generate a codeword, which is transmitted on the channel.