Polar Code Puncturing That Preserves Reliability Order
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Solution Overview
Problem
Existing methods for generating polar codes of lengths other than N = 2^m suffer from performance degradation, especially for large K and small R, and require additional rate-matching techniques that complicate the construction of polar codes with good performance across various dimensions.
Innovation Solution
The proposed method involves puncturing bits in a way that preserves the reliability order of the code sequence, allowing for the construction of polar codes of any given length without recalculation of bit reliabilities, using a puncturing scheme that determines the number of removed bits based on predefined parameters and a lookup table.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If BRMIAA rate-matching scheme with block puncturing is used to construct polar codes of length N ≠ 2^m, then code length flexibility is improved, but performance degrades for large K and small R
Solution Approach 1:
The patent pre-calculates and stores the reliability order of bit positions for the full N_max = 2^m code length before any puncturing occurs. This preliminary determination of reliability order allows the system to selectively puncture bits while maintaining optimal performance characteristics, resolving the contradiction between code length flexibility and code performance
Solution Approach 2:
The patent changes the parameter being punctured from arbitrary or uniformly distributed bits to specifically selected bit positions based on pre-calculated reliability order. By changing which bits are punctured (parameter selection) rather than how many bits are punctured, the system maintains performance while achieving flexible code lengths
2Reliability
If reliability recalculation is performed to construct polar codes of different lengths, then code performance is improved, but computational complexity increases
Solution Approach 1:
The patent performs reliability calculation in advance for the full N_max length code and stores the results. When constructing polar codes of any shorter length N < N_max, the system simply uses the pre-calculated reliability order from the full-length code, eliminating the need for repeated reliability calculations and significantly reducing computational complexity
Solution Approach 2:
The pre-calculated reliability order for the full N_max length code serves as a universal reference for constructing polar codes of any length N ≤ N_max. This single pre-computation enables multiple code constructions with different lengths and rates without requiring separate reliability calculations for each case
3Ease of manufacture
If bit reversal permutation is applied to determine shortened bits, then construction simplicity is improved, but code performance deteriorates for low code rates
Solution Approach 1:
The patent changes the selection criterion for punctured bits from position-based (bit reversal permutation indices) to reliability-based (bits with lowest reliability scores). This parameter change ensures that the most unreliable bits are punctured, optimizing code performance while maintaining reasonable construction complexity
Data Source
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AI summary
The present invention relates to a device (202b, 204b) for generating a polar code of length N and dimension K on the basis of an original polar code being defined by a code sequence S having N max bit indices sorted from least reliable to most reliable sub-channels. The device (202b, 204b) comprises a processing unit (202c, 204c) configured to: (a) generate an auxiliary code sequence having N max /2 bit indices by removing bit indices greater than or equal to N max /2 from the code sequence S; (b) remove from the auxiliary code sequence the last N R bit indices to generate a modified auxiliary code sequence, wherein N R denotes the number of removed bits and wherein the processing unit (202c, 204c) is configured to determine the number of removed bits N R on the basis of N ma x, N and a predefined code rate R; and (c) generate the polar code of length N and dimension K by puncturing the original polar code on the basis of a puncturing set defined by the last p=N max -N bit indices of the modified auxiliary code sequence. Moreover, the invention relates to a corresponding method for generating a polar code.