# On the Error Probability of Short Concatenated Polar and Cyclic Codes with Interleaving

## TL;DR

This paper analyzes the error performance of short concatenated polar and cyclic codes with interleaving, providing bounds on error rates and emphasizing the importance of outer code optimization for low error floors.

## Contribution

It introduces a new ensemble model for concatenated polar and cyclic codes with interleaving, enabling derivation of error bounds under maximum likelihood decoding.

## Key findings

- Bounds on achievable error rates are derived.
- Interleaving impacts the error performance and code optimization.
- Outer cyclic code design is crucial for low error floors.

## Abstract

In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is employed together with an inner systematic polar code. A concatenated code ensemble is introduced placing an interleaver at the input of the polar encoder. The introduced ensemble allows deriving bounds on the achievable error rates under maximum likelihood decoding, by applying the union bound to the (expurgated) average weight enumerators. The analysis suggests the need of careful optimization of the outer code, to attain low error floors.