Polar Code Generation Using Distance Spectrum Row Selection
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Solution Overview
Problem
Existing polar code generation methods are limited by restricted code lengths to powers of 2, leading to high complexity and latency, especially for short codes, and lack practicality due to the need for complex density evolution algorithms and inefficient puncturing or shortening techniques, which result in suboptimal block error rate performance.
Innovation Solution
A method for generating polar codes using a processor to create a distance spectrum vector based on a kernel matrix, allowing for the determination of information bit indices to achieve improved distance properties, enabling the generation of polar codes with flexible lengths and reduced complexity through a simpler row selection algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If classical polar codes with kernel T2 are used, then code length is restricted to powers of 2, but encoding complexity and latency increase for non-power-of-2 lengths
Solution Approach 1:
The patent segments the code length requirement by using different kernels (T2 and T3) for different segments of the code construction. This allows flexible code lengths that are not restricted to powers of 2, while maintaining manageable encoding complexity through modular kernel-based construction.
Solution Approach 2:
The patent changes the kernel parameter from fixed T2 to variable kernels (T2 and T3) that can be selected based on the desired code length. This parameter change enables adaptation to different code lengths without proportionally increasing encoding complexity.
2Reliability
If density evolution algorithms are used to determine bit reliability, then information bit indices can be optimized, but computational complexity and latency increase significantly
Solution Approach 1:
The patent uses a simplified, less computationally intensive method to determine information bit indices compared to the full density evolution algorithm. This disposable approximation achieves acceptable reliability without the high computational cost, enabling practical implementation.
Solution Approach 2:
The patent changes the approach from using complex density evolution algorithms to using simpler metrics or pre-computed tables for determining bit reliability. This parameter change reduces computational complexity while maintaining sufficient reliability for practical applications.
3Adaptability or versatility
If puncturing or shortening techniques are used to achieve non-power-of-2 code lengths, then code length flexibility improves, but block error rate performance deteriorates
Solution Approach 1:
The patent performs preliminary action by carefully selecting the information bit indices using the proposed method before encoding. This preliminary optimization of bit selection compensates for the non-power-of-2 code length, maintaining good block error rate performance without requiring puncturing or shortening techniques.
Data Source
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AI summary
The invention relates to an apparatus (110a) and method for generating a polar code c N of length N and dimension K, on the basis of a generator matrix G N of size N x N, wherein the generator matrix G N is based on a kernel T p of size p x p, with p ≤ N, wherein the polar code c N is given by c N = u N ⋅ G N , wherein u N = (u 0 ,..., u N-1 ) is a vector of size N, u i ,i = 0,... N - 1, corresponding to an information bit if i ∈ /, / being a set of K information bit indices, and u i = 0, if ί ∈ F, F being a set of N - K frozen bit indices. The apparatus (110a) comprises a processor (110a-1) configured to: generate a distance spectrum vector d Tp = ( d Tp (1),..., d Tp (p)) of size p of the kernel Tρ, wherein d Tp (h), h = 1,..., p, corresponds to a maximum value among all possible minimum distances of all possible polar codes of size p and dimension h generated on the basis of the kernel T p , generate a distance spectrum vector d GN of size N of the generator matrix G N on the basis of the distance spectrum vector d Tp , determine the set of K information bit indices / on the basis of the distance spectrum vector d GN , and generate the polar code c N on the basis of the set of K information bit indices /.