# Finite Blocklength Rates over a Fading Channel with CSIT and CSIR

## TL;DR

This paper derives bounds on the maximum transmission rate for finite blocklength codes over a fading AWGN channel with CSI at both transmitter and receiver, highlighting the impact of CSI on rate performance.

## Contribution

It provides new finite blocklength bounds that quantify the rate deviations from capacity and the benefits of CSI at the transmitter in fading channels.

## Key findings

- Bounds quantify finite blocklength rate deviations from capacity.
- CSI at the transmitter enhances achievable rates.
- Numerical examples illustrate the bounds and rate improvements.

## Abstract

In this work, we obtain lower and upper bounds on the maximal transmission rate at a given codeword length $n$, average probability of error $\epsilon$ and power constraint $\bar{P}$, over a finite valued, block fading additive white Gaussian noise (AWGN) channel with channel state information (CSI) at the transmitter and the receiver. These bounds characterize deviation of the finite blocklength coding rates from the channel capacity which is in turn achieved by the water filling power allocation across time. The bounds obtained also characterize the rate enhancement possible due to the CSI at the transmitter in the finite blocklength regime. The results are further elucidated via numerical examples.