LDPC Parity Check Matrix Masking for Low-Complexity Encoding
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Solution Overview
Problem
Conventional LDPC code systems face challenges in generating irregular parity check matrices with non-uniform weight distributions, requiring additional circuitry for generator matrices and increased complexity with multiple encoding rates, leading to performance degradation and increased circuit scale.
Innovation Solution
A check-matrix generating method that involves creating a mask matrix to convert regular quasi-cyclic matrices into irregular matrices with an LDGM structure, eliminating the need for generator matrices and reducing circuit complexity by applying a masking rule to ensure a predetermined minimum loop in the parity check matrix.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional LDPC code systems use regular quasi-cyclic matrices for encoding, then the encoding structure is simple and circuit implementation is straightforward, but the performance degrades due to uniform weight distributions and short loops
Solution Approach 1:
The patent introduces a mask matrix as an intermediary element that, when applied to the regular quasi-cyclic parity check matrix, transforms it into an irregular matrix with improved weight distribution. This mask matrix acts as a mediator that modifies the structure without requiring complete redesign of the encoding system, thereby improving decoding performance while maintaining reasonable circuit complexity
Solution Approach 2:
The patent applies local modifications to specific elements of the parity check matrix by using a mask matrix that selectively changes weights in certain positions. This creates an irregular matrix with non-uniform weight distributions in critical areas, improving performance by addressing specific structural weaknesses (short loops and uniform weights) rather than redesigning the entire matrix
2Adaptability or versatility
If generator matrices are added to improve encoding capability, then the flexibility and performance of the system increase, but the circuit scale and complexity increase significantly
Solution Approach 1:
The patent makes the parity check matrix H multi-functional by designing it to simultaneously serve both decoding operations and encoding operations. Through the LDGM structure with staircase-form submatrices, the same matrix H enables both functions without requiring separate generator matrices, thereby maintaining encoding flexibility while significantly reducing circuit scale
Solution Approach 2:
The patent merges the functions of the parity check matrix and generator matrix into a single structure. By organizing H into an LDGM structure where specific submatrices are in staircase form, the system combines what were previously separate components (check matrix for decoding, generator matrix for encoding) into one unified matrix that performs both roles
3Adaptability or versatility
If multiple parity check matrices are prepared for different encoding rates, then the system can handle various rates, but the circuit scale and complexity increase
Solution Approach 1:
The patent introduces dynamic configurability to the single parity check matrix H through the use of selectable submatrices. Different combinations of submatrices can be activated based on the desired encoding rate, allowing the system to adapt to various rates without requiring separate matrices for each rate, thus maintaining versatility while reducing circuit complexity
Data Source
AI summary
A regular quasi-cyclic matrix is prepared, a conditional expression for assuring a predetermined minimum loop in a parity check matrix is derived, and a mask matrix for converting a specific cyclic permutation matrix into a zero-matrix based on the conditional expression and a predetermined weight distribution is generated. The specific cyclic permutation matrix is converted into the zero-matrix to generate an irregular masking quasi-cyclic matrix. An irregular parity check matrix in which the masking quasi-cyclic matrix and a matrix in which the cyclic permutation matrices are arranged in a staircase manner are arranged in a predetermined location.