Mixed-Kernel Polar Code Construction for Flexible Block Lengths
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Solution Overview
Problem
Polar codes with the original construction are restricted to code lengths that are powers of 2, limiting their flexibility and error correction capability, and puncturing or shortening techniques, while providing flexibility, increase decoding complexity and degrade error rate performance.
Innovation Solution
A mixed-Kernel construction for polar codes using Kernels of different dimensions to generate block lengths not restricted to powers of integers, reducing complexity and improving error-rate performance by allowing more flexible code lengths without significant loss in performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If puncturing or shortening techniques are used to achieve flexible code lengths, then code length flexibility is improved, but decoding complexity increases and error rate performance degrades
Solution Approach 1:
The patent segments the code construction process by using different Kernels (T2 for powers of 2, Tl for other lengths) to handle different code length requirements. This segmentation allows the system to achieve code length flexibility without applying puncturing or shortening techniques, thereby avoiding the associated increase in decoding complexity and performance degradation.
2Adaptability or versatility
If puncturing or shortening techniques are used to achieve flexible code lengths, then code length flexibility is improved, but error rate performance deteriorates
Solution Approach 1:
The patent segments the code construction approach to use appropriate Kernels for different code length scenarios. By using Tl Kernels for non-power-of-2 lengths, the system achieves code length flexibility while maintaining optimal error rate performance, avoiding the performance deterioration caused by puncturing or shortening techniques.
Solution Approach 2:
The patent changes the fundamental parameter of the Kernel dimension from fixed (T2 only) to variable (Tl for any l). This parameter change enables direct construction of polar codes for any code length N = l^n without requiring puncturing or shortening, thereby maintaining error rate performance while achieving code length flexibility.
3Reliability
If original polar code construction with T2 Kernel is used, then error rate performance is maintained, but code length is restricted to powers of 2
Solution Approach 1:
The patent changes the Kernel dimension parameter from fixed (T2) to variable (Tl where l can be any integer). This parameter change allows the construction of polar codes with lengths N = l^n for any l, not just powers of 2, while maintaining good error rate performance through proper Kernel selection and design.
Solution Approach 2:
The patent creates a universal polar code construction framework that can handle both traditional power-of-2 lengths (using T2 Kernel) and non-power-of-2 lengths (using Tl Kernel). This multi-functional approach maintains error rate performance across different code length scenarios while providing code length flexibility.
Data Source
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AI summary
A communication device (40) comprises a code constructor (41) and a channel encoder (42). The channel encoder (42) is configures to encode a number of input symbols u to a number of output symbols x using a polar code of a code length N with a transformation matrix GN. The code constructor (41) is configured to compose the transformation matrix GN from at least two different polar code Kernels.