Generating a Regular LDPC Code Teaching-Research Matrix with Optimized Parameters

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Resource Overview

Generate a regular LDPC code teaching-research matrix H with rows (preferably larger) equal to half the number of columns, row weight of 6, column weight of 3, and ensuring no cycles of girth 4 between any two rows. Implementation method: H = HGrandom2(m, n), where m represents the number of rows and n represents the number of columns. The algorithm employs a random construction approach while maintaining structural constraints through girth checking mechanisms.

Detailed Documentation

In this implementation, we need to generate a regular LDPC code teaching-research matrix H. For optimal performance, the matrix should have the number of rows equal to half the number of columns, with each row having a weight of 6 and each column having a weight of 3. Additionally, we must ensure that there are no cycles of girth 4 between any two rows. The matrix generation utilizes the function call: H = HGrandom2(m, n), where m represents the row count and n represents the column count. This function implements a structured random construction algorithm that first initializes the matrix with specified row and column weights, then iteratively checks and eliminates short cycles using permutation techniques and bipartite graph validations. Through this method, we can generate a compliant regular LDPC code teaching-research matrix H suitable for both educational demonstrations and research applications in coding theory.

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