Analysis of LT Codes with Unequal Recovery Time

TL;DR

This paper analyzes LT codes with unequal recovery time, revealing their redundancy issues and proposing a feedback-based modification to improve decoding efficiency for lower priority segments.

Contribution

It provides the first probabilistic analysis of redundancy in LT codes with unequal recovery time and introduces a feedback mechanism to enhance decoding performance.

Findings

LT codes with unequal recovery time cause high redundancy in lower priority segments.

A single feedback improves decoding efficiency significantly.

The analysis offers new insights into the probabilistic behavior of these codes.

Abstract

In this paper we analyze a specific class of rateless codes, called LT codes with unequal recovery time. These codes provide the option of prioritizing different segments of the transmitted data over other. The result is that segments are decoded in stages during the rateless transmission, where higher prioritized segments are decoded at lower overhead. Our analysis focuses on quantifying the expected amount of received symbols, which are redundant already upon arrival, i.e. all input symbols contained in the received symbols have already been decoded. This analysis gives novel insights into the probabilistic mechanisms of LT codes with unequal recovery time, which has not yet been available in the literature. We show that while these rateless codes successfully provide the unequal recovery time, they do so at a significant price in terms of redundancy in the lower prioritized segments. We propose and analyze a modification where a single intermediate feedback is transmitted, when the first segment is decoded in a code with two segments. Our analysis shows that this modification provides a dramatic improvement on the decoding performance of the lower prioritized segment.