# Polar Codes over Fading Channels with Power and Delay Constraints

## TL;DR

This paper proposes a practical polar coding scheme for fading channels with power and delay constraints, using channel inversion and capacity analysis to improve reliability in wireless communications.

## Contribution

It introduces a novel polar coding approach for fading channels with power constraints, including a method to determine the optimal code rate under these conditions.

## Key findings

- Polar codes can achieve the symmetric capacity of the equivalent channel.
- A practical scheme with channel inversion mitigates fading effects.
- Method to compute optimal polar code rate under power constraints.

## Abstract

The inherent nature of polar codes being channel specific makes it difficult to use them in a setting where the communication channel changes with time. In particular, to be able to use polar codes in a wireless scenario, varying attenuation due to fading needs to be mitigated. To the best of our knowledge, there has been no comprehensive work in this direction thus far. In this work, a practical scheme involving channel inversion with the knowledge of the channel state at the transmitter, is proposed. An additional practical constraint on the permissible average and peak power is imposed, which in turn makes the channel equivalent to an additive white Gaussian noise (AWGN) channel cascaded with an erasure channel. It is shown that the constructed polar code could be made to achieve the symmetric capacity of this channel. Further, a means to compute the optimal design rate of the polar code for a given power constraint is also discussed.