Block-Punctured Polar Codes Without Reliability Recalculation
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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 small code rates and low code dimensions, due to the limitations of reliability re-calculation, bit reversal shortening, and group puncturing techniques.
Innovation Solution
A method that preserves the reliability order of bits in the code sequence by generating an auxiliary code sequence and removing specific indices to create a puncturing set, allowing for the construction of polar codes of any length without recalculation of bit reliabilities, using equations such as NR=round(ap+b) to determine the number of removed bits based on Nmax, N, and the code rate R.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If bit reversal shortening is used to construct polar codes of any length, then code length flexibility is improved, but decoding performance deteriorates for low code rates
Solution Approach 1:
The code sequence is divided into two parts: an upper N/2 bits and a lower N/2 bits. The puncturing is applied selectively to one of these parts based on the code rate, allowing flexible code length adaptation while preserving the reliability of the other part for low code rates.
Solution Approach 2:
Different parts of the code sequence are treated differently based on their reliability characteristics. The upper and lower N/2 bits are evaluated separately, and puncturing is applied only to the less reliable part, preserving the quality of the more reliable part for low code rate scenarios.
2Adaptability or versatility
If group puncturing is used to construct polar codes of different lengths, then code length adaptability is improved, but decoding performance deteriorates for rates from 1/4 to 2/5
Solution Approach 1:
The puncturing configuration is dynamically adjusted based on the code rate. For code rates from 1/4 to 2/5, the method selectively applies puncturing only to the upper or lower N/2 bits rather than both, adapting the puncturing intensity to match the code rate requirements and avoid excessive performance degradation.
3Adaptability or versatility
If BRMIAA rate-matching scheme with block puncturing is used, then code construction flexibility is improved, but performance degrades for large K and small R
Solution Approach 1:
Instead of applying full block puncturing to both upper and lower N/2 bits, the method applies puncturing partially to only one of these parts. This partial action approach provides sufficient code length flexibility while avoiding the excessive performance degradation that occurs when both parts are heavily punctured, especially for large K and small R scenarios.
Data Source
AI summary
The device and method disclosed herein are configured 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 Nmax bit indices sorted from least reliable to most reliable sub-channels. The device comprises a processing unit configured to: (a) generate an auxiliary code sequence having Nmax/2 bit indices by removing bit indices greater than or equal to Nmax/2 from the code sequence S; (b) remove from the auxiliary code sequence the last NR bit indices to generate a modified auxiliary code sequence; 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=Nmax−N bit indices of the modified auxiliary code sequence.