Polar Code Repolarization for Flexible Length and Channel Reliability
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Solution Overview
Problem
Polar codes are limited by code length restrictions to powers of 2, leading to increased system complexity and reduced error correction performance due to changes in output channel reliability, especially when unreliable channels are used for information transmission.
Innovation Solution
Establishing multiple polarization matrices and performing repolarization on specific input channels to enhance channel reliability, allowing for code lengths not restricted to powers of 2 and improving error correction by reassigning output bits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the code length of polar code is restricted to the power of 2, then the polarization matrix structure is simplified, but the system complexity increases and code length flexibility is reduced
Solution Approach 1:
The patent divides the coding system into multiple polarization matrices, each handling a portion of the code length. This segmentation allows the system to achieve arbitrary code lengths by combining multiple matrices while maintaining manageable complexity for each individual matrix.
Solution Approach 2:
The patent introduces a new dimension of code construction by using multiple polarization matrices arranged in a hierarchical structure, transitioning from a single-matrix approach to a multi-matrix architecture that enables flexible code length selection.
2Adaptability or versatility
If the output channel states change, then the channel conditions adapt to different scenarios, but the reliability ranking of input bit channels changes requiring re-polarization
Solution Approach 1:
The patent implements a dynamic re-polarization mechanism that adjusts the polarization matrices based on the actual output channel states. This dynamic adaptation ensures that the input bit channels maintain optimal reliability rankings even when channel conditions change, by selectively applying re-polarization to affected channels.
Solution Approach 2:
The system incorporates feedback from the output channel states to determine whether re-polarization is needed. By monitoring the channel conditions and using this information to guide the re-polarization process, the system maintains reliability while adapting to changing environments.
3Reliability
If re-polarization is performed on specific input channels, then channel reliability is improved, but the system complexity increases due to additional processing
Solution Approach 1:
The patent applies re-polarization selectively to only those input channels that require reliability improvement, rather than uniformly processing all channels. This localized approach focuses computational resources on specific channels with reliability issues, reducing overall processing complexity while maintaining necessary reliability enhancements.
Solution Approach 2:
The system performs partial re-polarization on only the necessary portion of input channels rather than complete re-polarization of all channels. This partial action approach achieves the required reliability improvement with reduced processing complexity by targeting only the channels that need enhancement.
Data Source
AI summary
A method for generating a polar code includes the steps of: establishing a plurality of polarization matrices that receive a plurality of first input bits via a plurality of first input channels and provide a plurality of first output bits on a plurality of first output channels; selecting at least one to-be-enhanced input channel from the first input channels of the polarization matrices; providing a re-polarization matrix that receives a plurality of second input bits via a plurality of second input channels and provides a plurality of second output bits on a plurality of second output channels, wherein a part of the second output bits is used as the first output bit(s) on the at least one to-be-enhanced input channel; and providing a polar code that comprises the first output bits and a remaining part of the second output bits.