Universal Polar Code Construction via Bit-Channel Sorting
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Solution Overview
Problem
Constructing polar codes that are universally good for an arbitrary class of channels is challenging due to the difficulty in identifying good bit-channels, as existing methods are channel-specific and do not account for variations in underlying channel characteristics, leading to suboptimal performance across different channels.
Innovation Solution
A method for constructing a universal polar code by sorting bit-channel indices based on their error probabilities, identifying the smallest error probabilities to determine good bit-channels that maintain an aggregate error probability below a target frame error rate, ensuring robust performance across all channels in a given class.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polar codes are optimized for a certain channel, then performance on that channel is improved, but performance on other channels deteriorates
Solution Approach 1:
The patent applies universality by constructing a single polar code that functions effectively across multiple different channel types. Instead of creating separate optimized codes for each channel, the invention develops a universal code construction method that achieves reliable communication on various channels including BSC, BEC, and AWGN channels simultaneously.
Solution Approach 2:
The patent employs parameter changes by transforming the channel representation from specific channel characteristics to capacity-based parameters. By expressing channels in terms of their capacity and using capacity-achieving distributions, the code construction becomes adaptable to different channel types without requiring channel-specific optimization.
2Device complexity
If heuristic and approximate algorithms are used for polar code construction, then construction complexity is reduced, but the codes are only good for one given channel and not universally applicable
Solution Approach 1:
The patent resolves this contradiction by creating a universal code construction algorithm that works across different channels while maintaining computational efficiency. The method uses capacity-based channel representation and a unified construction approach that achieves both low complexity and broad applicability.
Solution Approach 2:
The invention transforms the code construction problem from channel-specific parameters to capacity-based parameters, enabling a single algorithm to handle multiple channel types. This parameter transformation allows the construction algorithm to be universally applicable without increasing complexity.
3Manufacturing precision
If polar code construction depends on underlying channel characteristics, then optimization for that channel is achieved, but the code may not be good for transmission over another channel
Solution Approach 1:
The patent resolves this contradiction by changing the construction parameters from detailed channel characteristics to capacity-based parameters. This abstraction allows precise code construction that adapts to different channels through their capacity values rather than requiring channel-specific optimization details.
Solution Approach 2:
The invention introduces dynamics by making the code construction adaptable to different channel conditions through capacity parameters. The construction method dynamically adjusts to various channel types while maintaining a unified framework, allowing the same code to perform well across channel variations.
Data Source
AI summary
An apparatus and method of constructing a universal polar code is provided. The apparatus includes a first function block configured to polarize and degrade a class of channels Wj to determine a probability of error Pe,j of each bit-channel of Wj, wherein jε{1, 2, . . . , s}, in accordance with a bit-channel index i; a second function block configured to determine a probability of error Pe(i) for the universal polar code for each bit-channel index i; a third function block configured to sort the Pe(i); and a fourth function block configured to determine a largest number k of bit-channels such that a sum of corresponding k bit-channel error probabilities Pe(i) is less than or equal to a target frame error rate Pt for the universal polar code, wherein the indices corresponding to the k smallest Pe(i) are good bit-channels for the universal polar code.