# Design of Polar Codes for Parallel Channels with an Average Power Constraint

## TL;DR

This paper proposes a novel polar code design for parallel BiAWGN channels that optimizes power allocation and bit-to-channel mapping to maximize mutual information, resulting in improved performance under average power constraints.

## Contribution

It introduces a polar code design tailored for parallel channels with optimized power allocation and bit mapping, demonstrating gains over traditional methods.

## Key findings

- Power allocation specific to polar codes yields significant performance gains.
- Optimized bit-to-channel mapping improves mutual information sum.
- The approach enhances polar code efficiency under average power constraints.

## Abstract

Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and the power allocation under the average power constraint. Information theory suggests to allocate power such that the sum of mutual information (MI) terms is maximized. However, a power allocation specific to polar codes shows significant gains.