How to Modify Polar Codes for List Decoding

Abstract

Polar codes are constructed based on the reliability of bit-channels. This construction suits the successive cancellation (SC) decoding, where one error in the successive estimation of the bits fails the decoding. However, in SC list (SCL) decoding, the correct path may remain in the list by tolerating multiple penalties. This characteristic of list decoding demands a different approach in code construction.In this work, we modify the conventional construction by a greedy search algorithm in which a bit-swapping approach is employed to re-distribute the low-reliability bits in the subblocks aiming for a reduction in the probability of correct path elimination. The numerical results for polar codes of length 1 kb under CRC-aided SCL decoding show improvements of about 0.4 dB for R=0.8 and over 0.2 dB for R=0.5 at L=32.