A Search Method for Large Polarization Kernels

Abstract

A new search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing depth-first search combined with some methods which reduce the search space. Using the proposed method, we improved almost all existing lower bounds on the maximum rate of polarization for kernels of size from 17 to 27.We also obtain kernels which admit low complexity processing by the recently proposed recursive trellis algorithm. Numerical results demonstrate the advantage of polar codes with the proposed kernels compared with shortened polar codes and polar codes with small kernels.

Shortened Polarization Kernels

“…2: Performance of (768, 384) polar codes Fig. 2 illustrates the performance of different (768, 384) polar codes decoded by SCL decoder with list size L. We report the results for s P ⋆ (K 32 ) ⊗ F 5 , F 5 ⊗ K 24 and T 3 ⊗ F 8 MK PSCs, where K 24 is a 24 × 24 kernel and T 3 is a 3 × 3 kernel introduced in [27] and [15] respectively . We also include the results for descending (DES) asymmetric construction with 16-bit CRC [3] and improved hybrid design [7] of MK polar codes.…”