On the Concatenation of Non-Binary Random Linear Fountain Codes with Maximum Distance Separable Codes

TL;DR

This paper introduces a new fountain coding scheme combining MDS block codes with LRFC codes over the same field, analyzing its performance and showing its advantages at different erasure probabilities.

Contribution

It presents a novel concatenation of MDS and LRFC codes over $F_q$, with derived bounds on decoding failure probabilities, enhancing fountain code performance analysis.

Findings

Performs as well as LRFC codes at high erasure probabilities.

Lower failure probabilities by several orders of magnitude at moderate/low erasure probabilities.

Provides tight bounds on decoding failure probability as a function of overhead.

Abstract

A novel fountain coding scheme has been introduced. The scheme consists of a parallel concatenation of a MDS block code with a LRFC code, both constructed over the same field, $F_q$. The performance of the concatenated fountain coding scheme has been analyzed through derivation of tight bounds on the probability of decoding failure as a function of the overhead. It has been shown how the concatenated scheme performs as well as LRFC codes in channels characterized by high erasure probabilities, whereas they provide failure probabilities lower by several orders of magnitude at moderate/low erasure probabilities.