On the Effects of Kernel Configuration in Multi-Kernel Polar Codes

Area of Science:

• Coding Theory
• Information Theory
• Wireless Communications

Background:

• Polar codes are capacity-achieving linear block codes known for low-complexity implementation.
• Existing methods limit polar code lengths to powers of two, necessitating advanced kernel designs.
• Designing optimal polar codes for specific 5G systems is challenging due to numerous design parameters.

Purpose of the Study:

• To extend the analysis of the scaled DTS-parameter (SDTS-parameter) for multi-kernel polar codes.
• To validate the applicability of the SDTS-parameter in the design of multi-kernel polar codes.
• To provide a structured design technique for optimal polarization circuits in advanced communication systems.

Main Methods:

• Formalized a recursive technique for designing higher-order polarization kernels from smaller ones.
• Utilized the scaled DTS-parameter (SDTS-parameter, ζ) for analytical assessment.
• Extended the SDTS-parameter analysis to multi-kernel polar codes.

Main Results:

• The SDTS-parameter was validated for single-kernel polar codes.
• The study demonstrates the applicability of the SDTS-parameter for multi-kernel polar codes.
• A structured approach for designing optimal multi-kernel polar codes is presented.

Conclusions:

• The SDTS-parameter is a valuable tool for analyzing and designing multi-kernel polar codes.
• This work enhances the flexibility and usability of polar codes in practical 5G applications.
• The findings contribute to the development of more efficient and adaptable wireless communication systems.