Recursive Descriptions of Polar Codes

TL;DR

This paper presents a recursive formalization of polar codes and their decoding algorithms, enabling easier development and hardware implementation for various kernels.

Contribution

It introduces a recursive description framework for polar codes and decoding algorithms, applicable to arbitrary kernels and facilitating hardware design.

Findings

Recursive descriptions simplify decoding algorithm development.

Hardware architectures are effectively designed using the recursive approach.

Applicable to both standard and arbitrary polarizing kernels.

Abstract

Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. Using such description allows an easy development of these algorithms for arbitrary polarizing kernels. Hardware architectures for these decoding algorithms are also described in a recursive way, both for Arikan's standard polar codes and for arbitrary polarizing kernels.