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, making them insufficient for modem communication systems, and existing methods like puncturing and shortening techniques suffer from high latency, lack of structure, and performance loss.
Innovation Solution
A device and method that generate polar codes by combining reliability and minimum distance constructions using transformation matrices based on kernel matrices, allowing for flexible code length generation and improved error-rate performance.
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 implementation complexity and latency increase due to lack of structure in frozen sets and puncturing patterns
Solution Approach 1:
The polar code construction is segmented into multiple kernels (e.g., T2, T3, T4) of different dimensions. Each kernel can be independently selected and combined to achieve desired code lengths. This segmentation allows systematic generation of codes with lengths not restricted to powers of 2, while maintaining structural regularity that simplifies implementation compared to ad-hoc puncturing/shortening methods.
Solution Approach 2:
The patent employs nested kernel structures where smaller kernels are embedded within larger transformation matrices. The transformation matrix GN is constructed as a Kronecker product of multiple kernels (e.g., G12 = T2 ⊗ T2 ⊗ T3), creating a hierarchical nested structure that enables systematic code generation with arbitrary lengths while preserving the polar code's fundamental properties and reducing implementation complexity.
2Adaptability 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
Solution Approach 1:
The frozen sets and information sets are predetermined and systematically designed before code generation, based on the selected kernel combination. This preliminary design ensures optimal error-rate performance by pre-identifying reliable bit positions through polarization analysis, avoiding the performance degradation associated with ad-hoc puncturing or shortening applied after code generation.
Solution Approach 2:
The patent changes the fundamental parameter of kernel dimension selection to achieve arbitrary code lengths. By selecting different combinations of kernels with dimensions 2, 3, 4, etc., the total code length can be flexibly adjusted (e.g., N=12 using T2⊗T2⊗T3) while maintaining optimal error-rate performance through systematic frozen set design, avoiding the performance loss of puncturing/shortening techniques.
3Adaptability or versatility
If multi-kernel constructions are used to achieve arbitrary code lengths, then code length flexibility is improved, but construction complexity increases due to multiple kernels of different dimensions
Solution Approach 1:
The patent develops a universal framework using a set of standard kernels (T2, T3, T4, etc.) that can be combined in various ways to generate polar codes of arbitrary lengths. This universal kernel library approach simplifies construction complexity by providing reusable building blocks, eliminating the need to design custom codes for each length, and enabling systematic generation through Kronecker products of standardized kernels.
Data Source
AI summary
The present disclosure relates to a device for generating a polar code xN of length N and dimension K on the basis of a transformation matrix GN of size N×N, wherein the transformation matrix GN is based on a first matrix GN, of size Nr×N, and on a second matrix GN<sub2>d </sub2>of size Nd×Nd, wherein N=Nr·Nd, and wherein the polar code xN is given by xN=uN·GN, wherein uN=(u0, . . . uN-1) is a vector of size N, an element ui, i=0, . . . N−1, of the vector corresponding to an information bit if i∈I, I being a set of K information bit indices, and ui=0, if i∈F, F being a set of N−K frozen bit indices.