On The Weight Distribution of Fixed-Rate Raptor Codes

TL;DR

This paper analyzes the weight distribution of fixed-rate Raptor codes, deriving formulas for their average distance spectrum and conditions for positive minimum distance, which are crucial for their error-correcting performance.

Contribution

It provides a new analytical expression for the average distance spectrum and establishes conditions for positive minimum distance in fixed-rate Raptor code ensembles.

Findings

Derived the average distance spectrum expression.

Established the asymptotic exponent of the weight distribution.

Identified conditions for strictly positive typical minimum distance.

Abstract

In this paper Raptor code ensembles with linear random precodes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight distribution. The asymptotic growth rate analysis is then exploited to develop a necessary and sufficient condition under which the fixed-rate Raptor code ensemble exhibits a strictly positive typical minimum distance.