# Weight Distributions for Successive Cancellation Decoding of Polar Codes

## TL;DR

This paper derives exact weight distributions during successive cancellation decoding of polar codes, providing insights into error probability estimates and the structure of the decoding process.

## Contribution

It introduces the exact weight distributions at each decoding stage, linking them to error analysis and partial order of synthetic channels, advancing understanding of polar code decoding.

## Key findings

- Derived exact weight distributions for each decoding stage
- Linked weight distribution components to decoding error probability
- Established minimal distance between cosets for different decoding paths

## Abstract

In this paper, we derive the exact weight distributions that emerge during each stage of successive cancellation decoding of polar codes. Though we do not compute the distance spectrum of polar codes, the results allow us to get an estimate of the decoding error probability and to show a link between the first nonzero components of the weight distribution and the partial order between the synthetic channels. Also, we establish the minimal distance between two cosets associated with two paths that differ in two positions. This can be regarded as a first step toward analyzing the weight distributions for the successive cancellation list decoding.