Irregular Polar Code Encoding for Short-Block Error Correction
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Solution Overview
Problem
Polar codes, despite asymptotically achieving optimal coding efficiency, face inferior performance at finite codeword lengths and have high computational complexity, limiting their adaptability to non-uniform reliability channels and modulation schemes.
Innovation Solution
The introduction of irregular polar codes with additional parameters such as irregular coupling values, permutation irregularity, and de-activated XOR operations, along with joint optimization of interleavers and polar code construction, to enhance error correction performance and reduce complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If regular polar codes are used, then coding efficiency is improved asymptotically, but error correction performance deteriorates at finite codeword lengths
Solution Approach 1:
The patent applies local quality by introducing irregular polar codes where different portions of the code structure have different properties. Specifically, the code uses non-uniform coupling values and selective deactivation of XOR operations at different stages, creating local variations in the code structure that optimize performance for finite block lengths while maintaining overall coding efficiency.
Solution Approach 2:
The patent changes key parameters of the polar code structure by introducing irregular coupling values instead of uniform coupling, and by selectively deactivating XOR operations at different stages. These parameter changes transform the regular polar code into an irregular polar code that achieves better error correction performance at finite codeword lengths while adapting to non-uniform channel characteristics.
2Reliability
If regular polar codes are used, then coding efficiency is improved, but computational complexity increases
Solution Approach 1:
The patent applies the taking out principle by selectively removing (deactivating) certain XOR operations from the regular polar code structure. By extracting and disabling specific XOR operations at selected stages, the computational complexity is reduced while maintaining the essential error correction functionality and coding efficiency of polar codes.
Solution Approach 2:
The patent changes the operational parameters of the polar code by introducing selective deactivation of XOR operations. This parameter change transforms the full-complexity regular polar code into an irregular polar code with reduced computational requirements, achieving a balance between coding efficiency and computational complexity.
3Reliability
If regular polar codes are used, then theoretical capacity is achieved asymptotically, but adaptability to non-uniform channels deteriorates
Solution Approach 1:
The patent applies local quality by creating irregular polar codes with non-uniform coupling values and selective XOR operation deactivation. These local variations in code structure allow the code to adapt to non-uniform channel characteristics, where different bit positions experience different reliability levels, while still achieving theoretical capacity asymptotically.
Solution Approach 2:
The patent introduces dynamics into the polar code structure by using irregular coupling values and selective deactivation patterns that can be adapted to different channel conditions. This dynamic approach allows the code to optimize its structure for non-uniform channels while maintaining the fundamental polar code properties that enable asymptotic capacity achievement.
Data Source
AI summary
A transmitter for transmitting an encoded codeword over a communication channel is described. The transmitter includes a source to accept source data, an irregular polar encoder operated by a processor to encode the source data with at least one polar code to produce an encoded codeword, a modulator to modulate the encoded codeword, and a front end to transmit the modulated and encoded codeword over the communication channel, wherein the polar code is specified by a set of regular parameters and a set of irregular parameters.