Block-Circulant LDPC Encoding with Low-Complexity ARA Structure
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Solution Overview
Problem
Existing block-circulant LDPC codes face challenges in direct expansion into structured block-circulant codes without introducing low-weight codewords, and existing encoders for these codes are complex and inefficient in hardware implementation.
Innovation Solution
The development of novel encoders and encoding methods for block-circulant LDPC codes using accumulate-repeat-accumulate codes with repetition, iterative encoding techniques, and block-circulant generator matrices, which allow for efficient encoding and hardware implementation by leveraging the block-circulant structure of the parity check matrix.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Shape
If block-circulant LDPC codes are directly expanded into structured block-circulant codes, then code structure is improved, but low-weight codewords are introduced which deteriorate error correction performance
Solution Approach 1:
The code construction is segmented into multiple stages: first constructing a base LDPC code with good error correction properties, then separately designing the block-circulant structure. This segmentation allows the base code to maintain high weight codewords while the block-circulant expansion provides the desired structured shape, resolving the contradiction between structure and performance.
Solution Approach 2:
The patent applies different construction strategies to different parts of the code. The base matrix is designed with specific properties to avoid low-weight codewords, while the block-circulant expansion is applied locally to specific submatrices. This local quality approach allows the code to have structured block-circulant form in certain regions while maintaining high error correction performance through careful base matrix design.
2Adaptability or versatility
If complex encoders are used for block-circulant LDPC codes, then encoding capability is improved, but hardware implementation complexity increases
Solution Approach 1:
The patent extracts and utilizes the inherent block-circulant structure properties to simplify the encoder design. By recognizing that block-circulant matrices have repeated patterns, the encoder only needs to store and process one circulant matrix, extracting the essential encoding capability while removing redundant computational complexity. This allows sophisticated encoding capability with reduced hardware complexity.
Solution Approach 2:
The encoder is designed to handle multiple code rates and configurations using a universal block-circulant structure. The same encoder architecture can encode different LDPC codes by changing the base matrix and circulant size, providing multi-functionality. This universal design achieves high adaptability without proportionally increasing hardware complexity, as the underlying structure remains the same.
3Productivity
If high-speed encoding is implemented, then productivity is improved, but encoding accuracy may deteriorate
Solution Approach 1:
The patent performs preliminary organization of the encoding computations by pre-structuring the block-circulant matrices and pre-calculating certain transformation steps. This preliminary action allows the encoder to operate at high speed by avoiding complex real-time computations, while the pre-structured approach ensures encoding accuracy is maintained. The block-circulant structure itself serves as a preliminary organization that speeds up processing without sacrificing precision.
Data Source
AI summary
Methods and apparatus to encode message input symbols in accordance with an accumulate-repeat-accumulate code with repetition three or four are disclosed. Block circulant matrices are used. A first method and apparatus make use of the block-circulant structure of the parity check matrix. A second method and apparatus use block-circulant generator matrices.