Structured LDPC Parity-Check Matrix for Flexible Code Rates
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Solution Overview
Problem
Existing LDPC code designs face challenges in achieving high throughput and low latency while preserving simple encoding features, and they struggle with flexible rate adjustments through shortening and puncturing without degrading coding gain or disturbing weight distributions.
Innovation Solution
The method involves constructing structured base parity check matrices using sub-matrices such as permutation, pseudo-permutation, and zero matrices, and expanding these matrices to maintain structural properties, allowing for efficient decoding and flexible rate adjustments by shortening or puncturing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If base parity check matrices are designed to follow assumed degree distribution, then decoding performance is improved, but the number of sub-matrix blocks becomes large which reduces throughput
Solution Approach 1:
The base parity check matrix is segmented into sub-matrices with specific structures (permutation matrices, zero matrices, and identity matrices). This segmentation allows the matrix to be processed in smaller blocks during expansion, reducing the number of sub-matrix blocks while preserving the degree distribution properties needed for decoding performance.
Solution Approach 2:
The invention changes the structural parameters of the base parity check matrix by using specific patterns of permutation matrices and zero matrices. This allows the matrix to maintain optimal degree distribution for decoding while having fewer sub-matrix blocks, thereby increasing throughput without sacrificing reliability.
2Adaptability or versatility
If row combining is used to increase code rate, then code rate is improved, but the base parity matrix remains relatively large which affects decoding time
Solution Approach 1:
The base parity check matrix is divided into smaller sub-matrices with specific structures. This segmentation reduces the overall size of the base matrix while allowing row combining to achieve higher code rates. The segmented structure enables more efficient processing during decoding, reducing decoding time despite the increased code rate.
3Adaptability or versatility
If shortening and puncturing are applied to adjust code rate, then rate flexibility is improved, but weight distribution is disturbed which degrades performance
Solution Approach 1:
The invention uses specific parameter choices in the base parity check matrix structure (permutation matrices and zero matrices arranged in particular patterns) that make the matrix more resilient to shortening and puncturing operations. This allows rate adjustment while better preserving the weight distribution and maintaining coding gain compared to conventional matrices.
Data Source
AI summary
A method for constructing a low-density parity-check (LDPC) code using a structured base parity check matrix with permutation matrix, pseudo-permutation matrix, or zero matrix as constituent sub-matrices; and expanding the structured base parity check matrix into an expanded parity check matrix. A method for constructing a LDPC code using a structured base parity check matrix H=[Hd|Hp], Hd is the data portion, and Hp is the parity portion of the parity check matrix; the parity portion of the structured base parity check matrix is such so that when expanded, an inverse of the parity portion of the expanded parity check matrix is sparse; and expanding the structured base parity check matrix into an expanded parity check matrix. A method for encoding variable sized data by using the expanded LDPC code; and applying shortening, puncturing.