LDPC Parity Check Matrix Layout for Low-Complexity Encoding
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Solution Overview
Problem
LDPC codes face complexity issues in coding and decoding due to the lack of structure in their parity check matrices, particularly with randomly generated matrices, which complicates the calculation of redundancy bits and requires significant storage, leading to performance degradation at low error rates.
Innovation Solution
A method for constructing an LDPC code using a structured parity check matrix with two matrix areas: a processing matrix, a connection matrix with only one '1' per column and row, and a triangular matrix, allowing for parallel processing and simplified coding while maintaining a sufficient minimum distance for good performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a randomly generated parity check matrix is used for LDPC coding, then coding flexibility is improved, but coding complexity and storage requirements increase significantly
Solution Approach 1:
The parity check matrix H is segmented into two distinct areas: H1 (M×K matrix associated with information bits) and Hp (M×M square matrix associated with parity bits). This segmentation allows each submatrix to have optimized properties - H1 can be randomly generated for flexibility while Hp is structured (diagonal or triangular) for simplified inversion and calculation, thus resolving the contradiction between flexibility and complexity
Solution Approach 2:
Different parts of the parity check matrix are assigned different structural qualities. The H1 area maintains random generation for coding flexibility and performance, while the Hp area implements a deterministic structured form (diagonal or triangular) that enables simple inversion and fast calculation. This local differentiation resolves the contradiction by applying appropriate structural properties to different functional areas
2Device complexity
If a structured parity check matrix is used for LDPC coding, then coding complexity is reduced, but minimum distance and error rate performance deteriorate
Solution Approach 1:
The matrix is segmented so that H1 maintains random structure for good error rate performance and minimum distance, while Hp uses structured form for simplicity. The random H1 ensures sufficient minimum distance and reliability, while structured Hp reduces complexity - resolving the contradiction between reliability and complexity
Solution Approach 2:
The H1 area is assigned random quality for reliability and minimum distance, while the Hp area is assigned structured quality for low complexity. This local quality differentiation allows the system to achieve both high reliability and low complexity simultaneously
3Speed
If a pseudodeterministic parity check matrix with triangular Hp is used, then calculation speed is improved, but storage requirements and structural organization increase
Solution Approach 1:
The parity check matrix is segmented into H1 and Hp, where Hp is structured as diagonal or triangular. This segmentation enables fast calculation through simple inversion of Hp while the segmented structure itself can be stored efficiently, reducing overall storage requirements compared to storing a complete random matrix
Solution Approach 2:
The Hp area is assigned triangular or diagonal structure that enables fast inversion and calculation, while the segmented organization allows efficient storage. The local structural quality in Hp provides calculation speed without proportionally increasing storage requirements
Data Source
AI summary
A communication method and a communication system including a first entity (3) including an information source (9) and a coder device (11) connected by a channel (7) transmitting data to a second entity (5) including a decoder device (13), the coder device (11) coding a data sequence sent by the information source (9) to form a set of code words from a parity check matrix including two matrix areas, each matrix area including a processing matrix, a connecting matrix including only one “1” per column and only one “1” per row, and a triangular matrix, and the decoder device (13) decoding a coded reception signal that is received by the second entity and is derived from the set of code words constructed in accordance with said parity check matrix.