Polar Code Bit Distribution with Rate-Adaptive β-Weighting
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Solution Overview
Problem
Existing algorithms for polar code construction are computationally inefficient and introduce undesirable features, making them suboptimal for allocating frozen and information bits in polar codes.
Innovation Solution
The implementation of enhanced Polarization Weighting (PW) methodology, which uses a generalized β-expansion to determine the reliability of bit positions and strategically select a multiplicative factor based on the coding rate, allowing for more accurate and efficient allocation of information bits in polar codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing algorithms for polar code construction are used, then the allocation of frozen and information bits can be performed, but the computational efficiency is poor and undesirable features are introduced
Solution Approach 1:
The patent changes the parameter β (beta) in the β-expansion formula based on the coding rate. Specifically, β is set to 2^(1/m) where m is selected from {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} depending on the coding rate. This dynamic parameter adjustment allows the algorithm to adapt to different coding scenarios, improving both computational efficiency and allocation accuracy without requiring complex computations for each case.
Solution Approach 2:
The patent pre-determines the ordered sequence q based on the selected β value before actual polar code construction. By performing the β-expansion and sorting operations in advance, the method avoids repeated computational overhead during the encoding process. The pre-computed ordered sequence is then directly applied to allocate information bits, significantly improving computational efficiency while maintaining allocation accuracy.
2Ease of operation
If a fixed β-expansion method is used, then the implementation is simple, but the accuracy in approximating exact channel reliabilities deteriorates at varying code rates
Solution Approach 1:
The patent introduces dynamics into the β-expansion method by making β variable rather than fixed. The value of β = 2^(1/m) changes according to the coding rate, allowing the approximation accuracy to adapt to different code rates and block sizes. This dynamic adjustment maintains the simplicity of the β-expansion approach while significantly improving the accuracy of channel reliability approximation across varying operational conditions.
Solution Approach 2:
By changing the parameter β based on coding rate requirements, the patent achieves high accuracy in approximating exact channel reliabilities. The selected m values from the set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} correspond to different coding rate scenarios, ensuring optimal approximation accuracy for each case while maintaining computational tractability.
3Adaptability or versatility
If existing methods like FRANK are used, then scalability may be achieved, but limitations remain in computational efficiency and accuracy
Solution Approach 1:
The patent creates a universal method that works across different coding rates, block sizes, and scalability requirements through the β-expansion approach. By selecting appropriate m values, the same fundamental algorithm adapts to various scenarios without requiring separate specialized methods. This universal approach eliminates the limitations of existing methods like FRANK while maintaining scalability, as the β-expansion can be applied to polar codes of any length and coding rate.
Data Source
AI summary
Methods and devices are described for determining reliabilities of bit positions in a bit sequence for information bit allocation using polar codes. The reliabilities are calculated using a weighted summation over a binary expansion of each bit position, wherein the summation is weighted by an exponential factor that is selected based at least in part on the coding rate of the polar code. Information bits and frozen bits are allocated to the bit positions based on the determined reliabilities, and data is polar encoded as the information bits. The polar encoded data is then transmitted to a remote device.