Performance and Construction of Polar Codes on Symmetric Binary-Input Memoryless Channels

TL;DR

This paper introduces a linear-complexity construction method for polar codes on symmetric binary-input channels and derives new bounds on their block error probability, improving efficiency and understanding of polar code performance.

Contribution

A novel linear-time construction method for polar codes on symmetric channels and new bounds on block error probability are presented, advancing code design and analysis.

Findings

Construction complexity reduced to linear in blocklength.

New upper and lower bounds for block error probability.

Enhanced understanding of polar code performance on symmetric channels.

Abstract

Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed. Furthermore, new upper and lower bounds of the block error probability of polar codes are derived for the BEC and the arbitrary symmetric B-MC, respectively.