Polar Code Check Equation Mapping for Reliable Decoding
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Solution Overview
Problem
Current polar coding methods lack a method to improve performance by adding a check equation, which is essential for enhancing reliability and decoding efficiency in communications systems.
Innovation Solution
A simple method to construct a check equation by determining the correspondence between subchannels based on preset values, where the check bit and information bit positions are defined by sequence numbers satisfying specific remainder conditions, allowing for efficient coding with low overheads.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If polar coding is used to achieve channel capacity with good performance and low decoding complexity, then decoding complexity is reduced, but reliability improvement through check equations is not available
Solution Approach 1:
The code is segmented into information bits and check bits with distinct roles. Information bits carry data while check bits provide redundancy for error detection and correction, enabling reliability improvement without increasing overall decoding complexity of the polar code structure
Solution Approach 2:
Check equations serve as intermediary mechanisms that connect transmitted bits with received bits. These equations provide a verification layer that enhances reliability by enabling error detection and correction while maintaining the low-complexity polar decoding framework
2Reliability
If check equations are added to improve polar code performance, then reliability is improved, but coding complexity and overhead increase
Solution Approach 1:
Check equations are applied locally to specific subsets of bits rather than globally to all bits. This selective application provides reliability improvement where needed while minimizing the increase in coding complexity and overhead
Solution Approach 2:
The parameters of check equations (such as check bit positions, equation coefficients, and redundancy ratios) are optimized to achieve the desired reliability level with minimal overhead. By carefully selecting these parameters, the system improves reliability while controlling coding complexity
3Reliability
If check equations are added to improve polar code performance, then reliability is improved, but overhead increases
Solution Approach 1:
Instead of adding check equations for all bits, the method applies check equations to only the necessary portion of bits. This partial application provides sufficient reliability improvement while minimizing the overhead introduced by check bits and check equation processing
Data Source
AI summary
Embodiments of the present invention disclose a coding method. The method in the embodiments of the present invention includes: constructing a check equation based on a correspondence between a first subchannel and a second subchannel that is in a second subchannel group, where a check bit of the check equation corresponds to the first subchannel, an information bit of the check equation corresponds to the second subchannel, the second subchannel group includes at least one second subchannel, a sequence number of the first subchannel is divided by a first preset value and a remainder is a second preset value, a sequence number of the second subchannel is divided by a third preset value and a remainder is a fourth preset value, and the sequence number of the first subchannel is greater than the sequence number of the second subchannel; and performing coding by using the check equation.