Adaptive Segmented Aggregation and Rate Assignment Techniques for Flexible-Length Polar Codes

Abstract

Polar codes have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provable capacity achieving capability. They have been standardized to be used for encoding information on the control channels in 5G wireless networks due to their robustness for short codeword lengths. The conventional approach to generate polar codes is to recursively use 2×2 kernels and polarize channel capacities. This approach however, has a limitation of only having the ability to generate codewords of length Norig=2n form. In order to mitigate this limitation, multiple techniques have been developed, e.g., polarization kernels of larger sizes, multi-kernel polar codes, and downsizing techniques like puncturing or shortening. However, the availability of so many design options and parameters, in turn makes the choice of design parameters quite challenging. In this paper, the authors propose a novel polar code construction technique called Adaptive Segmented Aggregation which generates polar codewords of any arbitrary codeword length. This approach involves dividing the entire codeword into smaller segments that can be independently encoded and decoded, thereby aggregated for channel processing. Additionally a rate assignment methodology has been derived for the proposed technique, that is tuned to the design requirement.

Keywords

• polar codes
• puncturing
• shortening
• adaptive segmented aggregation
• rate-assignment