Design and Analysis of LT Codes with Decreasing Ripple Size

TL;DR

This paper introduces a novel LT code design that reduces decoding overhead by implementing a decreasing ripple size, supported by analytical insights and simulation results showing improved performance over existing methods.

Contribution

It proposes a new LT code design with decreasing ripple size during decoding, contrasting with previous constant ripple size approaches, leading to better efficiency.

Findings

Significant reduction in average overhead.

Lower error probability at fixed overhead.

Enhanced decoding performance compared to existing designs.

Abstract

In this paper we propose a new design of LT codes, which decreases the amount of necessary overhead in comparison to existing designs. The design focuses on a parameter of the LT decoding process called the ripple size. This parameter was also a key element in the design proposed in the original work by Luby. Specifically, Luby argued that an LT code should provide a constant ripple size during decoding. In this work we show that the ripple size should decrease during decoding, in order to reduce the necessary overhead. Initially we motivate this claim by analytical results related to the redundancy within an LT code. We then propose a new design procedure, which can provide any desired achievable decreasing ripple size. The new design procedure is evaluated and compared to the current state of the art through simulations. This reveals a significant increase in performance with respect to both average overhead and error probability at any fixed overhead.