A Tight Estimate for Decoding Error-Probability of LT Codes Using Kovalenko's Rank Distribution

TL;DR

This paper introduces a novel, less complex method for accurately estimating the decoding error probability of LT codes with dense rows using Kovalenko's rank distribution, enabling the design of near-optimal codes.

Contribution

It develops a new approach based on Kovalenko's rank distribution for estimating DEP of LT codes, improving accuracy and computational efficiency over existing methods.

Findings

Estimate closely matches Gaussian Elimination results

Method significantly reduces computational complexity

Enables design of dense-row LT codes near Kovalenko's rank limit

Abstract

A new approach for estimating the Decoding Error-Probability (DEP) of LT codes with dense rows is derived by using the conditional Kovalenko's rank distribution. The estimate by the proposed approach is very close to the DEP approximated by Gaussian Elimination, and is significantly less complex. As a key application, we utilize the estimates for obtaining optimal LT codes with dense rows, whose DEP is very close to the Kovalenko's Full-Rank Limit within a desired error-bound. Experimental evidences which show the viability of the estimates are also provided.