# Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design

## TL;DR

This paper provides a detailed analysis of inactivation decoding for LT and Raptor codes, introducing a first order analysis to predict inactivation counts and enabling optimized code design for better complexity-failure trade-offs.

## Contribution

It introduces a novel first order analytical framework for inactivation decoding, allowing precise control over decoding complexity and failure probability in LT and Raptor codes.

## Key findings

- Analytical expressions for expected inactivations
- Distribution of inactivation counts derived
- Numerical simulations confirm accuracy

## Abstract

In this paper we analyze LT and Raptor codes under inactivation decoding. A first order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of input symbols and the decoding overhead. The analysis is then extended to the calculation of the distribution of the number of inactivations. In both cases, random inactivation is assumed. The developed analytical tools are then exploited to design LT and Raptor codes, enabling a tight control on the decoding complexity vs. failure probability trade-off. The accuracy of the approach is confirmed by numerical simulations.