Performance and Construction of Polar Codes: The Perspective of Bit Error Probability

TL;DR

This paper introduces a new framework for analyzing and constructing polar codes focused on minimizing bit error probability, providing explicit, low-complexity metrics that outperform traditional methods.

Contribution

It develops a novel analysis of bit error probability for polar codes and proposes explicit construction metrics with linear complexity.

Findings

Proposed methods outperform conventional polar code constructions.

Derived upper bounds on bit error probability for polar codes.

Introduced efficient, explicit construction metrics for polar codes.

Abstract

Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new framework to analyze the bit error probability of polar codes. Specifically, by revisiting the error event of bit-channel, we first introduce the conditional bit error probability as a metric to evaluate the reliability of bit-channel for both systematic and non-systematic polar codes. Guided by the concept of polar subcode, we then derive an upper bound on the conditional bit error probability of each bit-channel, and accordingly, an upper bound on the bit error probability of polar codes. Based on these, two types of construction metrics aiming at minimizing the bit error probability of polar codes are proposed, which are of linear computational complexity and explicit forms. Simulation results show that the polar codes constructed by the proposed methods can outperform those constructed by the conventional methods.