Multi-Kernel Polar Code Matrix Permutation for Better Minimum Distance
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Solution Overview
Problem
Polar codes have limitations in code length flexibility, restricted to powers of 2, and limited minimum distance, which affects their performance in modern communication systems, especially for short lengths where error correction is crucial.
Innovation Solution
A device and method for generating multi-kernel polar codes through permutation of transformation matrices, maintaining the same decoding complexity and reliability, while improving minimum distance and error rates by permuting columns of sub-matrices to enhance polarization properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If original polar code construction is used, then code length is restricted to powers of 2, but this limitation reduces adaptability to diverse block lengths demanded by modern communication systems
Solution Approach 1:
The transformation matrix is segmented into multiple kernels of different dimensions, where each kernel operates on a specific stage of the encoding process. This segmentation allows the code length to be flexibly determined by the product of kernel dimensions, enabling non-power-of-2 lengths while maintaining a structured construction approach similar to original polar codes.
Solution Approach 2:
The code construction uses dynamic kernel selection where different kernels are applied at different stages based on the desired code length and rate. This dynamic approach allows the system to adapt to various communication requirements by selecting appropriate kernel combinations, providing versatility without requiring complete redesign for each code length.
2Adaptability or versatility
If multi-kernel construction is used to achieve flexible code lengths, then code length adaptability improves, but the minimum distance remains limited due to the Kronecker product structure
Solution Approach 1:
The invention applies different permutation operations to different stages of the encoding process, treating each stage with locally optimized properties. By permuting columns of transformation matrices at specific stages, the minimum distance is enhanced in those critical regions without affecting the overall flexible code length capability provided by the multi-kernel structure.
Solution Approach 2:
The invention changes the parameters of the transformation matrices through column permutation, which modifies the code's minimum distance while preserving the code length flexibility. By adjusting the permutation parameters at different stages, the system can optimize minimum distance for specific code lengths and rates without sacrificing the adaptability to diverse block lengths.
3Reliability
If column permutation is applied to increase minimum distance, then error correction performance improves, but decoding complexity may increase
Solution Approach 1:
The column permutation is performed in advance during the code construction phase, creating a pre-optimized transformation matrix structure. This preliminary action ensures that the minimum distance is maximized before the actual encoding and decoding operations, allowing the decoder to work with the already-optimized structure without adding significant computational overhead during the decoding process itself.
Data Source
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AI summary
The present invention relates to a device (102b, 104b) for generating a multi-kernel polar code ϰ N of length N and dimension K on the basis of a first transformation matrix G N of size N x N defining a first multi-kernel polar code. The device (102b, 104b) comprises a processor (102c, 104c) configured to generate a second transformation matrix G' N of size N x N by permuting the order of at least two columns of a sub-matrix of the first transformation matrix G N , and generate the multi-kernel polar code ϰ N on the basis of the following equation: ϰ N = u N ⋅ G' N , wherein u N = (u 0 ,..., u N-1 ) is a vector of size N, with the elements u i , i = 0,... N - 1, corresponding to an information bit if i ε /, / being a set of K information bit indices, and u i = 0, if i ε F, F being a set of N - K frozen bit indices.