Polar Code Construction Using Weight Spectra and Error Thresholds
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Solution Overview
Problem
The high computational complexity of constructing polar codes, particularly when signal-to-noise ratio changes, makes them impractical for real-world digital communication systems.
Innovation Solution
A method for constructing polar codes that calculates polar weight spectra and error probability thresholds using recursive relationships and MacWilliams identities, allowing for SNR-independent construction by sorting channels based on error probabilities and selecting appropriate channels for information and frozen bits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Gaussian approximation algorithm is used to construct polar codes per signal-to-noise ratio, then the error probabilities of polarized channels can be estimated, but the computational complexity increases significantly
Solution Approach 1:
The patent pre-calculates and stores polar weight spectra for different code lengths in a lookup table during system initialization. When constructing polar codes, the system directly retrieves pre-computed error probability threshold values based on code length and code rate, eliminating the need for real-time Gaussian approximation calculations. This preliminary action transforms complex runtime computations into simple table lookups, resolving the contradiction between estimation accuracy and computational complexity.
Solution Approach 2:
The patent uses MacWilliams identities to compute polar weight spectra from binary weight spectra through mathematical transformation. Instead of performing complex Gaussian approximation integrations, the system copies and transforms weight spectrum data using established mathematical relationships, significantly reducing computational burden while maintaining estimation accuracy.
2Reliability
If polar codes are constructed for each signal-to-noise ratio change, then accurate error probabilities are obtained, but practicality decreases due to high computational complexity
Solution Approach 1:
The patent creates a universal construction method that works across different signal-to-noise ratios by pre-computing polar weight spectra and error probability threshold values that are independent of specific SNR conditions. The lookup table stores universal characteristics of polar codes that can be applied to various transmission conditions, making the system both reliable and practically implementable without reconfiguration for each SNR change.
Solution Approach 2:
By performing all complex calculations during system initialization and storing results in lookup tables, the patent enables rapid polar code construction during actual operation. The preliminary computation phase separates heavy computational tasks from runtime operations, ensuring both accuracy and practicality in real-world deployments.
3Productivity
If recursive calculation of polar weight spectra is performed for code length 2N based on code length N, then computational efficiency improves, but implementation complexity increases
Solution Approach 1:
The patent divides the polar code construction process into hierarchical segments based on code lengths (N, 2N, 4N, etc.). Polar weight spectra for larger code lengths are recursively computed from smaller code lengths using established mathematical relationships. This segmentation allows efficient computation by breaking down complex problems into manageable sub-problems that can be solved incrementally and stored for future use.
Solution Approach 2:
The patent implements a nested structure where polar weight spectra for code length 2N are derived from spectra of code length N, which in turn are derived from length N/2, and so on. This nested approach reuses computational results across different code lengths, improving efficiency while organizing implementation complexity in a structured, manageable hierarchy.
Data Source
AI summary
A polar code construction method, apparatus, electronic device, and readable storage medium, applied to the field of wireless communication technology to reduce the complexity of polar code construction. The method comprises: calculating a weight spectrum corresponding to a polarized channel of a polar code with code length 2N based on the weight spectrum corresponding to the polarized channel with code length N, and MacWilliams identities; calculating, for each polarized channel, a union bound on the error probability of the polarized channel under the condition of additive white Gaussian noise based on the weight spectrum corresponding to the polarized channel and a union bound formula; determining the error probability threshold values based on the union bounds and a measurement method; sorting the error probability threshold values of all the polarized channels in ascending order, and selecting the polarized channels corresponding to the K smallest error probability threshold values.