LDPC Exponent Matrix Generation Using a Multi-Rate Table
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Solution Overview
Problem
State-of-the-art LDPC codes require dedicated exponent matrices for each code rate, leading to increased hardware storage requirements due to the need for specific exponent matrices for different code rates.
Innovation Solution
A method and system for generating a multi-rate table that allows the derivation of exponent matrices for various code rates, using a semi-random technique with a random sub-matrix and a semi-deterministic sub-matrix, where the first column vector of the semi-deterministic matrix has only three non-null elements, reducing the need for multiple stored exponent matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If dedicated exponent matrices are used for each code rate, then the LDPC decoding accuracy is improved, but the hardware storage requirements increase
Solution Approach 1:
A single multi-rate exponent matrix H_exp is designed to serve multiple code rates (R=1/2, 2/3, 3/4, 5/6, 7/8, 11/12, 15/16). The matrix has dimensions 162x10368 and can generate parity-check matrices for all these code rates through appropriate selection and combination of its rows and columns, eliminating the need for separate dedicated exponent matrices for each code rate.
Solution Approach 2:
The multi-rate exponent matrix is divided into multiple sub-matrices, each corresponding to a specific code rate. By segmenting the large 162x10368 matrix into smaller functional blocks, the system can selectively use only the required sub-matrix for the current code rate, reducing the effective storage and processing requirements while maintaining support for all code rates.
2Adaptability or versatility
If multiple dedicated exponent matrices are stored, then support for different code rates is ensured, but the device complexity increases
Solution Approach 1:
The system uses a single universal multi-rate exponent matrix that can generate parity-check matrices for all required code rates (R=1/2, 2/3, 3/4, 5/6, 7/8, 11/12, 15/16). This eliminates the need for multiple dedicated matrices and reduces device complexity while maintaining full code rate support.
Solution Approach 2:
The system dynamically selects and configures the appropriate sub-matrices from the multi-rate exponent matrix based on the current code rate requirement. This dynamic adaptation allows the same hardware structure to efficiently support different code rates without requiring separate dedicated exponent matrices for each rate.
Data Source
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AI summary
A method and a system for generating a multi-rate table for generating exponent matrixes for LDPC codes, said LDPC codes supporting different block sizes for each code rate Rj and being implemented with semi-random technique which requires that the exponent matrixes are composed of two sub-matrixes, a random sub-matrix and a semi-deterministic sub-matrix, wherein, conditions on column vector Cv, the first column vector of the semi-deterministic matrix, require that said column vector Cv has only three "non-null" elements with value different from "-1", which conventionally represents a null matrix, two of said three non-null elements being the first and the last element of the column vector Cv and the third non-null element being in a random position and having value "0" which represents the identity matrix, the invention comprising: - providing a random table having a column number nb and a row number rb; - dedicating for each code rate Rj, two rows of the random table to be processed; - generating the multi-rate table from said random table, by processing the elements of the two dedicated rows so as to satisfy said conditions on said column vector Cv.