Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes

TL;DR

This paper introduces a systematic method to balance decoding complexity and performance in polar codes by formulating an optimization problem and proposing an efficient greedy algorithm for large code lengths.

Contribution

It presents a novel optimization-based approach to enable fine-grained complexity-performance trade-offs in successive cancellation decoding of polar codes.

Findings

The method effectively reduces decoding complexity while maintaining performance.

The greedy algorithm efficiently solves the optimization problem for large code lengths.

The approach enhances the practical applicability of polar codes in various scenarios.

Abstract

Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications. Unfortunately, the successive nature of successive cancellation based decoders hinders fine-grained adaptation of the decoding complexity to design constraints and operating conditions. In this paper, we propose a systematic method for enabling complexity-performance trade-offs by constructing polar codes based on an optimization problem which minimizes the complexity under a suitably defined mutual information based performance constraint. Moreover, a low-complexity greedy algorithm is proposed in order to solve the optimization problem efficiently for very large code lengths.