LDPC Parity-Check Matrix Structure for Simpler Recursive Encoding
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Solution Overview
Problem
Existing LDPC codes face challenges in designing simple encoding algorithms due to non-uniform row weights and complex parity parts in their base parity check matrices, which complicates hardware implementation and scalability for various code rates and block sizes.
Innovation Solution
The method involves constructing a base parity check matrix with a structured parity check matrix by expanding each non-zero element into a shifted identity matrix and zero elements into zero matrices, allowing for recursive encoding and sparse inverse parity portions, thereby simplifying encoding and supporting various code rates and block sizes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a base parity check matrix with non-uniform row weights and complex parity parts is used, then the LDPC code can achieve certain error correction performance, but the encoding algorithm becomes complex and hardware implementation becomes difficult
Solution Approach 1:
The base parity check matrix is segmented into a data portion (Hd) and a parity portion (Hp), where the parity portion has a specific structure (identity matrix or shifted identity matrix) that enables simple recursive encoding. This segmentation allows the complex matrix to be handled through structured sub-components.
Solution Approach 2:
The invention changes the structural parameters of the parity portion of the base parity check matrix to have uniform or near-uniform row weights and specific patterns (identity/shifted identity matrices). This parameter optimization enables simple encoding algorithms while maintaining error correction performance.
2Adaptability or versatility
If the base parity check matrix is expanded to support various code rates and block sizes, then the LDPC code becomes more versatile, but the hardware redesign becomes significant
Solution Approach 1:
The base parity check matrix is designed with a universal structure where the parity portion consists of identity matrices or shifted identity matrices. This universal structure can be expanded to support multiple code rates (1/2, 2/3, 3/4, 5/6, 7/8) and various block sizes without fundamental hardware redesign, as the same encoding principles apply across different configurations.
Solution Approach 2:
The invention uses shifted identity matrices in the parity portion, where the shift amount can be dynamically adjusted to accommodate different code rates and block sizes. This dynamic parameter adjustment allows a single hardware architecture to adapt to multiple coding configurations without complete redesign.
3Reliability
If the parity portion of the base parity check matrix does not have a simple structure, then the LDPC code may achieve better error correction performance, but the encoding algorithm becomes computationally intensive
Solution Approach 1:
The parity portion is structured as identity matrices or shifted identity matrices, which are self-inverting (their inverse is themselves or easily computable). This self-service property allows the encoder to efficiently compute parity bits through simple operations without requiring complex matrix inversion, thereby improving encoding speed while maintaining performance.
Data Source
AI summary
Low density parity check code (LDPC) base parity check matrices and the method for use thereof in communication systems. The method of expanding the base check parity matrix is described. Examples of expanded LDPC codes with different code lengths and expansion factors are also shown.