Bounds on the Error Probability of Raptor Codes

TL;DR

This paper derives a tight upper bound on the decoding failure probability of q-ary Raptor codes under ML decoding, using the weight enumerator of the outer code, offering new analytical insights.

Contribution

It introduces a novel upper bound on Raptor code failure probability based on the outer code's weight enumerator, applicable to both fixed and random outer codes.

Findings

The bound is shown to be tight through simulations.

Provides a new analytical perspective similar to classical serial concatenation.

Enhances understanding of Raptor code performance under ML decoding.

Abstract

In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn randomly from some ensemble of codes. The bound is shown to be tight by means of simulations. This bound provides a new insight into Raptor codes since it shows how Raptor codes can be analyzed similarly to a classical fixed-rate serial concatenation.