Non-Binary QC-LDPC Parity Matrix Coding With Lower Storage
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Solution Overview
Problem
Non-binary LDPC codes face challenges with high storage space requirements and complex coding processes, hindering their application in communication systems with strict latency and reliability demands.
Innovation Solution
A coding method and device for non-binary quasi-cyclic LDPC codes, involving the determination of a base matrix with all-zero and cyclic shift elements, extension based on a lifting factor, and replacement of non-zero positions with non-binary values to generate a parity check matrix for efficient coding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-binary LDPC codes are used to improve coding gain and error correction performance, then reliability is improved, but storage space requirements increase and coding process complexity increases
Solution Approach 1:
The parity check matrix is segmented into a base matrix of size M_b×N_b that is extended to larger sizes using a lifting factor Z. The base matrix contains elements from a smaller set (0, 1, 2, ..., Z-1) that are systematically expanded to create the full parity check matrix, dividing the complex construction into manageable segments.
Solution Approach 2:
The patent changes the parameters of the parity check matrix by using a lifting factor Z to extend the base matrix dimensions. Instead of directly constructing large complex matrices, the system uses parameter Z to systematically generate larger matrices through repetition and transformation of the base matrix elements, reducing the complexity of parameter management.
2Reliability
If non-binary LDPC codes are used to improve coding gain, then reliability is improved, but storage space requirements increase
Solution Approach 1:
The base matrix is copied and extended Z times to generate the full parity check matrix. Instead of storing completely independent large matrices, the system stores a compact base matrix that is repeatedly copied and transformed, significantly reducing the storage space required while maintaining the non-binary code structure.
Solution Approach 2:
The base matrix serves as a nested structure that contains the fundamental pattern, which is then expanded through the lifting factor to create the full parity check matrix. The larger matrix is essentially a nested expansion of the smaller base matrix, allowing efficient storage of the compact base representation.
3Reliability
If non-binary values are used in the parity check matrix to improve error correction, then reliability is improved, but the coding process becomes more complex
Solution Approach 1:
The coding process is segmented into two stages: first constructing a simple base matrix with elements from a small field, then systematically extending it using the lifting factor. This segmentation makes the implementation easier by breaking down the complex non-binary coding into manageable steps with well-defined operations.
Solution Approach 2:
The patent uses parameter Z (lifting factor) to control the transition from the base matrix to the extended matrix. By changing this parameter, the system can systematically generate different code rates and lengths while maintaining a consistent construction methodology, simplifying the implementation of various non-binary codes.
Data Source
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AI summary
Embodiments of the present invention provide a coding method and device for a non-binary quasi-cyclic low density parity check (LDPC) code. The method comprises: determining a base matrix of a non-binary quasi-cyclic LDPC code, wherein the base matrix comprises a first element for indicating an all-zero square matrix and a second element for indicating a cyclic shift value of a unit matrix; extending the base matrix according to a lifting factor to obtain an extended matrix; obtaining a parity check matrix of the non-binary quasi-cyclic LDPC code according to non-binary values of non-zero positions in the extended matrix; and performing non-binary quasi-cyclic LDPC code coding on an input information bit sequence on the basis of the parity check matrix to obtain a sequence of codewords to be sent.