A Split-Reduced Successive Cancellation List Decoder for Polar Codes

TL;DR

This paper introduces a low complexity SCL decoding method for polar codes that reduces splitting by using a reliability-based rule and counters, maintaining performance while lowering computational effort.

Contribution

A novel splitting rule and counter-based pruning method are proposed, significantly reducing decoding complexity without sacrificing error performance in polar codes.

Findings

Achieves similar error performance to conventional SCL decoding.

Reduces decoding complexity substantially.

Validates the approach through simulation results.

Abstract

This paper focuses on low complexity successive cancellation list (SCL) decoding of polar codes. In particular, using the fact that splitting may be unnecessary when the reliability of decoding the unfrozen bit is sufficiently high, a novel splitting rule is proposed. Based on this rule, it is conjectured that, if the correct path survives at some stage, it tends to survive till termination without splitting with high probability. On the other hand, the incorrect paths are more likely to split at the following stages. Motivated by these observations, a simple counter that counts the successive number of stages without splitting is introduced for each decoding path to facilitate the identification of correct and incorrect path. Specifically, any path with counter value larger than a predefined threshold \omega is deemed to be the correct path, which will survive at the decoding stage, while other paths with counter value smaller than the threshold will be pruned, thereby reducing the decoding complexity. Furthermore, it is proved that there exists a unique unfrozen bit u_{N-K_1+1}, after which the successive cancellation decoder achieves the same error performance as the maximum likelihood decoder if all the prior unfrozen bits are correctly decoded, which enables further complexity reduction. Simulation results demonstrate that the proposed low complexity SCL decoder attains performance similar to that of the conventional SCL decoder, while achieving substantial complexity reduction.