Polar Code Generation Using Multi-Kernel Distance Spectrum Selection
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing polar code generation methods are complex and inefficient, particularly for short codes, due to their reliance on puncturing or shortening techniques that result in high latency and performance loss, and are limited by the need for code lengths that are powers of two, which do not suffice for modern communication systems.
Innovation Solution
A method for generating polar codes using a processor to create a distance spectrum vector based on a kernel Tp, allowing for the determination of information bit indices and the generation of polar codes with improved complexity and flexibility in code lengths, including those not restricted to powers of two, by employing a generator matrix constructed from Kronecker products of kernels like T3 and T5.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If puncturing or shortening techniques are used to achieve non-power-of-two code lengths, then code length flexibility is improved, but device complexity and latency increase due to lack of structured frozen sets and puncturing patterns
Solution Approach 1:
The patent changes the fundamental parameter of code construction by using multi-kernel generator matrices instead of single-kernel matrices. This allows code lengths that are not powers of two while maintaining structured frozen sets through the mathematical properties of Kronecker products of multiple kernels, thereby achieving code length flexibility without the complexity of ad-hoc puncturing patterns
Solution Approach 2:
The multi-kernel generator matrix construction provides a universal framework that handles both power-of-two and non-power-of-two code lengths through a single systematic approach. The same mathematical structure (Kronecker products of kernels) serves multiple functions: generating the generator matrix, determining frozen sets, and supporting various code lengths without requiring separate puncturing or shortening schemes
2Adaptability or versatility
If puncturing or shortening techniques are used to trim codes to any length, then code length adaptability is improved, but reliability deteriorates due to loss of performance compared to full codes
Solution Approach 1:
Instead of modifying existing power-of-two codes through puncturing or shortening, the patent changes the construction parameter by using multi-kernel generator matrices. This generates codes of any desired length directly with properly structured frozen sets, avoiding the performance degradation associated with removing bits from full codes
3Ease of manufacture
If classical polar code construction with single kernel T2 is used, then encoding simplicity is maintained, but code length is restricted to powers of two which limits versatility
Solution Approach 1:
The patent merges multiple kernels (T2, T3, T5, etc.) into a multi-kernel generator matrix construction. This combination maintains the simplicity of polar code encoding through the systematic use of Kronecker products while extending code length options beyond powers of two, as the product of kernels with different sizes generates codes of various lengths
4Reliability
If density evolution algorithms are used to determine information bit indices for short codes, then coding performance is improved, but processing time and complexity increase significantly
Solution Approach 1:
The patent performs preliminary action by pre-determining the generator matrix and frozen sets through multi-kernel construction before actual encoding. This avoids the need for real-time density evolution algorithms during short code generation, as the structured approach provides optimal or near-optimal frozen set configurations in advance through the mathematical properties of the kernel products
Data Source
AI summary
A method for generating a polar code cN of length N and dimension K, on the basis of a generator matrix GN of size N×N, is provided. The method includes generating a distance spectrum vector dT<sub2>p</sub2>=(dT<sub2>p</sub2>(1), . . . , dT<sub2>p</sub2>(p)) of size p of the kernel Tp, wherein dT<sub2>p</sub2>(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 Tp. The method also includes generating a distance spectrum vector dG<sub2>N </sub2>of size N of the generator matrix GN on the basis of the distance spectrum vector dT<sub2>p</sub2>, determining the set of K information bit indices I on the basis of the distance spectrum vector dG<sub2>N</sub2>, and generating the polar code cN on the basis of the set of K information bit indices I.