RC-LDPC Coding with Cyclic Matrix Weight Control for BER Stability
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Solution Overview
Problem
Existing RC-LDPC codes face difficulties in achieving favorable BER performance with high code rates, and the regularity of check matrices differs between the parity and information word parts, making it challenging to design codes that can efficiently handle multiple code rates.
Innovation Solution
The method involves adjusting the column weights of cyclic matrices in the check matrices to ensure 1<w0 and w1<w0, where w0 and w1 represent the maximum column weights for different code rates, allowing for all parity positions to be aligned on one side or at constant intervals, and maintaining a constant column weight for all code rates, ensuring self-orthogonality and a minimum Hamming distance of at least 6.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the maximum column weight of cyclic matrices is reduced for lower code rates, then BER performance is improved, but the regularity of check matrices becomes more difficult to maintain
Solution Approach 1:
The patent applies parameter changes by systematically adjusting the maximum column weight parameter (w1 < w0) of cyclic matrices based on code rate. For lower code rates, the maximum column weight is reduced to improve BER performance, while for higher code rates, the maximum column weight is increased to maintain good performance. This parameter adaptation resolves the contradiction by allowing the check matrix structure to be optimized for each specific code rate scenario.
Solution Approach 2:
The patent implements local quality by applying different maximum column weight constraints to different parts of the check matrix structure. Specifically, the information word part and parity part can have different column weight characteristics tailored to their respective requirements. This allows the check matrix to have locally optimized properties that simultaneously satisfy both BER performance requirements and regularity constraints across different code rates.
2Reliability
If different maximum column weights are used for different code rates, then BER performance is improved, but the complexity of coding device increases
Solution Approach 1:
The patent achieves universality by designing a coding device that can handle multiple code rates using a unified check matrix structure based on cyclic matrices. The device uses a systematic approach where the same basic structure (cyclic matrices with parameters p and q) serves all code rates, and the code rate is adjusted by changing the number of information bits k rather than requiring completely different structures. This multi-functional design reduces device complexity while maintaining improved BER performance across different code rates.
Solution Approach 2:
The patent uses parameter changes to enable a single coding device to adapt to different code rates by modifying parameters (k, p, q, w0, w1) rather than requiring separate devices. The check matrix structure remains consistent, but parameters are adjusted based on the desired code rate, allowing the device to efficiently support multiple code rates with improved BER performance without proportionally increasing complexity.
3Adaptability or versatility
If the number of cyclic matrices is increased to support more code rates, then adaptability is improved, but the device complexity increases
Solution Approach 1:
The patent implements universality by creating a check matrix structure that can support multiple code rates through a unified framework. The check matrix H is constructed using cyclic matrices with parameters p and q, where the same basic structure serves all code rates. The code rate is controlled by the number of information bits k, and the structure naturally adapts to different code rates without requiring fundamentally different constructions, thus improving adaptability while controlling complexity.
Solution Approach 2:
The patent applies segmentation by dividing the check matrix into cyclic matrix blocks with specific structures. The check matrix is segmented into information word parts and parity parts, each with tailored column weight constraints. This segmentation allows the system to support multiple code rates by adjusting the segmentation parameters rather than creating entirely new structures, thereby improving adaptability while managing device complexity.
Data Source
AI summary
The present invention relates to coding method and coding device that allow Rate-Compatible LDPC (low-density parity-check) codes to have favorable BER performance both with a low code rate and with a high code rate. In coding of LDPC codes that have plural code rates and whose all parity check matrices are composed of plural cyclic matrices, a coder 121 performs the coding in such a way that 1<w0 and w1<w0 are satisfied when the maximum column weight of the cyclic matrices in the check matrix of a certain code whose code rate is not the minimum value among the LDPC codes is defined as w0 and the maximum column weight of the cyclic matrices in the check matrix of a code having a code rate lower than that of the certain code is defined as w1.