Structured LDPC Parity-Check Matrix for Efficient Encoding and Decoding
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Solution Overview
Problem
There is a need for a method and apparatus to design a structured low-density parity-check (LDPC) code that achieves good error-correcting performance and can be efficiently encoded and decoded, as existing techniques lack a systematic approach for designing the base matrix and assigning permutation matrices for a given target H size.
Innovation Solution
A structured parity-check matrix H is proposed, where H is an expansion of a base matrix Hb, comprising a section Hb1 and a section Hb2, with Hb2 having a column with odd weight greater than 2 and matrix elements set to 1 for i=j, 1 for i=j+1, and 0 elsewhere, using identical submatrices for 1s and paired submatrices for an even number of 1s, to facilitate efficient encoding and decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a dense parity-check matrix H is used, then encoding and decoding can be performed, but error-correcting performance is poor and decoding complexity increases
Solution Approach 1:
The parity-check matrix H is segmented into a base matrix Hb of smaller dimensions with specific structured patterns. The base matrix is then expanded to form the full matrix H by replacing elements with permutation matrices, achieving both low density for simple decoding and good error correction performance
2Reliability
If a large parity-check matrix H is used to achieve good error-correcting performance, then memory requirements increase and implementation complexity increases
Solution Approach 1:
Instead of storing the entire large parity-check matrix H, the invention stores a compact base matrix Hb that can be systematically expanded. The base matrix serves as a template that is copied and transformed to generate the full matrix H, dramatically reducing memory requirements while maintaining the ability to perform encoding and decoding operations
3Quantity of substance
If a structured base matrix Hb is used, then memory requirements are reduced, but designing the base matrix and assigning permutation matrices for a given target H size becomes complex
Solution Approach 1:
The invention establishes specific parameter constraints for the base matrix Hb, including the structure of column hb with odd weight greater than 2, and the pattern of matrix elements where hi,j = 1 for i=j and i=j+1, and 0 elsewhere. These parameter specifications provide a systematic design methodology that reduces the complexity of creating structured LDPC codes for various target matrix sizes
Data Source
AI summary
A structured parity-check matrix H is proposed, wherein H is an expansion of a base matrix Hb and wherein Hb comprises a section Hb1 and a section Hb2, and wherein Hb2 comprises a first part comprising a column hb having an odd weight greater than 2, and a second part comprising matrix elements for row i, column j equal to 1 for i=j, 1 for i=j+1, and 0 elsewhere. The expansion of the base matrix Hb uses identical submatrices for 1s in each column of the second part H′b2, and the expansion uses paired submatrices for an even number of 1s in hb.