On the Origin of Polar Coding

TL;DR

This paper explains the original motivation behind polar coding, which was to enhance the cutoff rate of sequential decoding by splitting channels into subchannels, but it turned out to be effective on its own.

Contribution

It clarifies the cutoff rate considerations that led to the development of polar coding and its surprising effectiveness without needing outer codes.

Findings

Polar coding was initially designed to boost the cutoff rate of sequential decoding.

Polar codes proved highly effective, often eliminating the need for outer codes.

The paper elucidates the original motivation and theoretical basis of polar coding.

Abstract

Polar coding was conceived originally as a technique for boosting the cutoff rate of sequential decoding, along the lines of earlier schemes of Pinsker and Massey. The key idea in boosting the cutoff rate is to take a vector channel (either given or artificially built), split it into multiple correlated subchannels, and employ a separate sequential decoder on each subchannel. Polar coding was originally designed to be a low-complexity recursive channel combining and splitting operation of this type, to be used as the inner code in a concatenated scheme with outer convolutional coding and sequential decoding. However, the polar inner code turned out to be so effective that no outer code was actually needed to achieve the original aim of boosting the cutoff rate to channel capacity. This paper explains the cutoff rate considerations that motivated the development of polar coding.