Partial Quasi-Cyclic LDPC Encoding With Reduced Matrix Storage
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing LDPC codes that are not full row rank require more storage compared to their full row rank counterparts, limiting their efficiency in systems that need to store multiple codes, especially in programmable encoders where storage efficiency is crucial.
Innovation Solution
The technique involves generating LDPC encoded data using a parity generator matrix without the remainder matrix, allowing the generator matrix to be expressed in partial quasi-cyclic form, which reduces storage requirements and eliminates the need for extra circuitry, enabling efficient storage and encoding of both full and non-full row rank codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If non-full row rank LDPC codes are used, then coding flexibility and applicability are improved, but storage requirements increase
Solution Approach 1:
The generator matrix is segmented into distinct blocks: a quasi-cyclic portion and a remainder portion. This segmentation allows the system to separately handle the storage-efficient quasi-cyclic part while managing the remainder part through computational methods rather than full storage, thus resolving the contradiction between coding flexibility and storage requirements.
Solution Approach 2:
The remainder matrix is extracted and separated from the main quasi-cyclic generator matrix. By taking out this portion, the system can store only the essential quasi-cyclic structure efficiently while the extracted remainder is handled through computation during encoding, reducing overall storage requirements while maintaining coding flexibility.
2Reliability
If remainder matrix is included in generator matrix, then encoding accuracy is improved, but device complexity increases
Solution Approach 1:
The patent introduces an intermediary computational approach where the remainder matrix is not stored as part of the generator matrix but is computed on-demand during encoding operations. This intermediary method maintains encoding accuracy by preserving the mathematical relationship while avoiding the complexity of storing and processing the full remainder matrix in hardware.
Solution Approach 2:
Instead of storing the actual remainder matrix in hardware, the system creates computational copies or representations that can be regenerated as needed. This allows the encoding process to access remainder information when required for accuracy while avoiding the permanent storage and hardware complexity associated with the full remainder matrix.
3Quantity of substance
If full quasi-cyclic form is used, then storage efficiency is improved, but applicability to non-full row rank codes is limited
Solution Approach 1:
The patent applies local quality by making different parts of the generator matrix have different properties. The main body maintains strict quasi-cyclic structure for storage efficiency, while the remainder portion allows non-quasi-cyclic characteristics to enable applicability to non-full row rank codes. This local differentiation resolves the contradiction between storage efficiency and versatility.
Solution Approach 2:
The generator matrix structure is made asymmetric by distinguishing between the quasi-cyclic portion and the remainder portion. This asymmetric structure allows the system to exploit the storage efficiency of quasi-cyclic forms where applicable while accommodating the broader requirements of non-full row rank codes through the asymmetric remainder section, thus resolving the contradiction.
Data Source
AI summary
Encoding is performed by putting a low-density parity-check (LDPC) generator matrix into partial quasi-cyclic form comprising an identity matrix, a parity generator matrix, a zero matrix and a remainder matrix. The parity generator matrix is quasi-cyclic and the remainder matrix is not quasi-cyclic. An encoder is used to generate LDPC encoded data using the parity generator matrix and without using the remainder matrix.