Multi-Kernel Polar Code Construction for Flexible Length and Low Error Rate
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Solution Overview
Problem
The original construction of polar codes restricts code lengths to powers of 2, leading to limitations in modern communication systems, and existing methods like puncturing and shortening techniques suffer from high latency, lack of structure, and performance loss in error-rate performance, especially for medium-length codes.
Innovation Solution
A device and method that generate polar codes by combining reliability and minimum distance constructions using a transformation matrix based on multiple kernel matrices, allowing flexibility in code length and improving error-rate performance by determining information bit indices based on reliability and distance spectra.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If puncturing or shortening techniques are used to achieve arbitrary code lengths, then code length flexibility is improved, but error-rate performance deteriorates and implementation complexity increases
Solution Approach 1:
The transformation matrix is segmented into multiple kernel matrices of different dimensions (e.g., 2×2, 3×3, 4×4 kernels). By combining different numbers and types of kernels, polar codes can be constructed with arbitrary block lengths without requiring puncturing or shortening, thus maintaining both code length flexibility and error-rate performance.
2Adaptability or versatility
If puncturing or shortening techniques are used to achieve arbitrary code lengths, then code length flexibility is improved, but device complexity increases due to lack of structure in frozen sets
Solution Approach 1:
The patent establishes a universal construction framework using a library of kernel matrices that can generate polar codes of any block length. The frozen sets are constructed systematically using nested structures and mathematical formulas based on kernel dimensions, providing a unified and structured approach that simplifies implementation compared to ad-hoc puncturing or shortening methods.
3Adaptability or versatility
If multi-kernel constructions are used to achieve arbitrary code lengths, then code length flexibility is improved, but construction complexity increases when using solely reliability or solely distance constructions
Solution Approach 1:
The patent merges two construction approaches: reliability-based construction (using channel polarization and reliability vectors) and distance-based construction (using minimum distance criteria). By combining these methods, the patent achieves a balanced construction that maintains low complexity while improving block error rate performance for medium-length codes, avoiding the limitations of using either method alone.
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AI summary
The present invention relates to a device (102b, 104b) for generating a polar code ϰ N of length N and dimension K on the basis of a transformation matrix G N of size N x N, wherein the transformation matrix G N is based on a first matrix G N r of size N r x N r , and on a second matrix G Nd of size N d x N d , wherein N = N r ⋅ N d, and wherein the polar code ϰ N is given by ϰ N = υ N ⋅ G N , wherein υ N = (υ0,..., υ N -1)is a vector of size N, υ i ,i = 0,... N−1, corresponding to an information bit if i ε I, I being a set of K information bit indices, and υ i = 0, if i ε F, F being a set of N − K frozen bit indices. The device (102b, 104b) comprises a processor (102c, 104c) configured to generate a reliability vector v GNr = [v1,... v Nr ], wherein v i represents a reliability of an i-th input bit of a code generated by the first matrix G Nr , generate a distance spectrum vector d GNd = [d1,..., d Nd ] of a code generated by the second matrix G Nd , wherein d j represents a minimum distance of the code generated by the second matrix G Nd of dimension j, determine the set of K information bit indices I on the basis of the reliability vector v GNr and of the distance spectrum vector d GN , and generate the polar code c N on the basis of the set of K information bit indices I.