Polar Code Construction Using Error-Bound Reliability Sorting
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Solution Overview
Problem
The existing methods for calculating polarized channel reliability in polar code construction are inefficient, particularly under fading channels, due to the complexity of the Gaussian Approximation (GA) algorithm, which requires iterative recalculations of channel capacity and reliability when channel conditions change, such as signal-to-noise ratio variations.
Innovation Solution
A method that calculates the polar weight spectrum based on the code length, distribution probability density of fading factors, and signal-to-noise ratio to obtain an upper bound of error probability for each polarized channel, then uses logarithmic transformation to derive a reliability metric, sorting channels by reliability for efficient selection of noiseless and full-noise channels for information and frozen bits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the GA algorithm is used to calculate the reliability of each polarized channel under fading channels, then the reliability calculation can be performed, but the computational complexity is high and the calculation efficiency is low
Solution Approach 1:
The patent transforms the reliability calculation from using channel capacity as the metric to using the upper bound of error probability as the metric. This parameter change simplifies the calculation process by avoiding the need to traverse fading factors and recalculate when channel conditions change, thereby reducing computational complexity while maintaining reliability assessment capability
Solution Approach 2:
The patent employs an approximate upper bound of error probability calculation method that is computationally cheaper and sufficiently accurate for practical purposes, replacing the computationally expensive GA algorithm. This approximation approach provides adequate reliability assessment without requiring intensive computational resources
2Reliability
If the GA algorithm is used to calculate the reliability of each polarized channel, then the reliability can be obtained, but the calculation efficiency is low
Solution Approach 1:
The patent changes the calculation metric from channel capacity to upper bound of error probability, which can be computed directly without iterative procedures. This parameter transformation significantly improves calculation efficiency by eliminating the need to traverse fading factors and perform repeated calculations when channel conditions vary
Solution Approach 2:
The patent pre-calculates the upper bound of error probability using a closed-form expression that incorporates fading factor distribution and signal-to-noise ratio directly. This preliminary calculation approach avoids the need for real-time iterative computation, thereby enhancing calculation efficiency in dynamic channel conditions
3Reliability
If the GA algorithm requires iterative recalculations when channel conditions change, then the reliability can be updated, but the time consumption increases
Solution Approach 1:
The patent transforms the reliability metric to upper bound of error probability, which can be updated efficiently when channel conditions change by simply substituting new signal-to-noise ratio values into the closed-form expression. This parameter change eliminates the need for iterative recalibration, significantly reducing update time while maintaining reliability accuracy
Solution Approach 2:
The patent establishes a closed-form expression for the upper bound of error probability that incorporates fading factor distribution characteristics in advance. This preliminary formulation allows rapid updates when channel conditions change, as only the signal-to-noise ratio parameter needs to be updated without requiring full iterative recalculation
Data Source
AI summary
The embodiments of the present application provide a polar code construction method and apparatus, which relate to the field of communications technology. The method comprises: obtaining a polar weight spectrum for each polarized channel; calculating an upper bound of error probability of each polarized channel based on the obtained polar weight spectrum, distribution probability density of a fading factor of a fading channel, and a signal-to-noise ratio of the fading channel; taking a logarithm of the calculated upper bound of the error probability for each polarized channel and obtaining a reliability metric of the polarized channel based on the taken logarithm, wherein the smaller the metric value is, the higher the reliability of the polarized channel is; sorting all polarized channels in an ascending order of the reliability metric and selecting part of the polarized channels having a lowest reliability metric for transmitting information bits and the remaining polarized channels for transmitting frozen bits. According to the embodiments of the present application, performing polar code construction under the condition of a fading channel can improve the efficiency of polar code construction.