LDPC Parity Check Matrix Generation for Low-Storage Encoding
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Solution Overview
Problem
The wide use of Low Density Parity Check (LDPC) codes is limited due to the excessive storage space required for the sparse parity check matrix and the complexity of the encoding process.
Innovation Solution
The method generates the parity check matrix based on a generating sequence corresponding to a row generator, allowing for cyclic shift or direct addressing to minimize storage space, and uses this matrix to encode input data, reducing storage needs and simplifying the encoding process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the sparse parity check matrix is stored directly, then the encoding reliability is ensured, but the storage space requirement increases excessively
Solution Approach 1:
The patent extracts only the essential row generator information from the complete parity check matrix, storing merely the first row (or a minimal generating set) instead of the entire matrix. This extraction allows the full matrix to be regenerated on-demand, dramatically reducing storage requirements while preserving encoding capability.
Solution Approach 2:
The patent performs preliminary action by pre-defining the row generator structure and relationships during system design, so that the complete parity check matrix can be systematically constructed when needed. The row generator is prepared in advance with known mathematical relationships that enable efficient matrix reconstruction without storing the entire matrix.
2Reliability
If the traditional encoding process is used, then the error correction capability is achieved, but the encoding complexity increases
Solution Approach 1:
The patent extracts and utilizes only the row generator component for encoding operations, bypassing the need to construct and manipulate the complete parity check matrix during encoding. This extraction simplifies the encoding process to operations on the compact row generator representation, reducing computational complexity while maintaining error correction capability.
Solution Approach 2:
Instead of working with the full parity check matrix during encoding, the patent uses a simplified copy or representation (the row generator) that contains all necessary information for encoding. This copying approach allows encoding to proceed with reduced complexity while the full matrix structure is implied through the generator relationships.
3Manufacturing precision
If the complete parity check matrix is constructed and stored, then the encoding accuracy is maintained, but the storage efficiency decreases
Solution Approach 1:
The patent extracts the minimal sufficient information (row generator) needed to maintain encoding accuracy, eliminating redundant storage of the complete matrix. The extraction preserves all essential encoding relationships while removing unnecessary data, achieving both accuracy maintenance and storage efficiency improvement.
Solution Approach 2:
Instead of storing the complete parity check matrix and deriving generators from it, the patent inverts the approach by storing only the row generator and deriving the complete matrix structure when needed. This inversion fundamentally changes the storage paradigm from comprehensive to minimal, improving storage efficiency while preserving encoding accuracy through the generator's mathematical properties.
Data Source
AI summary
Disclosed is a method for data transmission, comprising: generating the parity check matrix on the basis of the generating sequence corresponded to the preserved row generator; encoding the input data by the generated matrix obtained by said parity check matrix, and obtaining the output data comprising the parity check information. Also provided in the present invention is an apparatus for data transmission. The method and apparatus of the present invention could make the parity check matrix take the minimum storage space.