Fountain Codes with Varying Probability Distributions

TL;DR

This paper introduces a novel approach to fountain codes using varying probability distributions, demonstrating significant overhead reduction by leveraging poset theory and dynamic distribution design.

Contribution

It shows that fixed probability distributions are unnecessary for fountain codes and develops a theoretical framework for non-constant distributions to minimize overhead.

Findings

Achieved up to 64% lower overhead than LT codes.

Developed a fundamental theory for designing non-constant probability distributions.

Proved that varying distributions can improve fountain code efficiency.

Abstract

Fountain codes are rateless erasure-correcting codes, i.e., an essentially infinite stream of encoded packets can be generated from a finite set of data packets. Several fountain codes have been proposed recently to minimize overhead, many of which involve modifications of the Luby transform (LT) code. These fountain codes, like the LT code, have the implicit assumption that the probability distribution is fixed throughout the encoding process. In this paper, we will use the theory of posets to show that this assumption is unnecessary, and by dropping it, we can achieve overhead reduction by as much as 64% lower than LT codes. We also present the fundamental theory of probability distribution designs for fountain codes with non-constant probability distributions that minimize overhead.