# Space-Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels

## TL;DR

This paper introduces a new method for designing space-time block codes and multilevel polar coded-modulation for slow fading broadcast channels, optimizing outage probability at moderate SNRs.

## Contribution

It develops outage optimality conditions, component code rate rules, and a joint optimization approach for short-to-moderate length polar codes and STBCs in non-ergodic channels.

## Key findings

- Derived outage optimality conditions for multistage decoding.
- Proposed a rate determination rule for component codes.
- Introduced a joint optimization method for polar codes and STBCs.

## Abstract

Slow fading broadcast channels can model a wide range of applications in wireless networks. Due to delay requirements and the unavailability of the channel state information at the transmitter (CSIT), these channels for many applications are non-ergodic. The appropriate measure for designing signals in non-ergodic channels is the outage probability. In this paper, we provide a method to optimize STBCs based on the outage probability at moderate SNRs. Multilevel polar coded-modulation is a new class of coded-modulation techniques that benefits from low complexity decoders and simple rate matching. In this paper, we derive the outage optimality condition for multistage decoding and propose a rule for determining component code rates. We also derive an upper bound on the outage probability of STBCs for designing the set-partitioning-based labelling. Finally, due to the optimality of the outage-minimized STBCs for long codes, we introduce a novel method for the joint optimization of short-to-moderate length polar codes and STBCs.