Kovalenko's Full-Rank Limit and Overhead as Lower Bounds for Error-Performances of LDPC and LT Codes over Binary Erasure Channels

TL;DR

This paper establishes Kovalenko's full-rank limit as a precise lower bound for decoding error probabilities and overheads in LDPC and LT codes over binary erasure channels, providing theoretical benchmarks.

Contribution

It introduces Kovalenko's full-rank limit as a new theoretical lower bound for error performance and overhead in LDPC and LT codes over BEC.

Findings

Kovalenko's limit is a tight lower bound for decoding error probability.

Derived a full-rank overhead as a lower bound for successful decoding.

Provides theoretical benchmarks for code performance over BEC.

Abstract

We present Kovalenko's full-rank limit as a tight lower bound for decoding error probability of LDPC codes and LT codes over BEC. From the limit, we derive a full-rank overhead as a lower bound for stable overheads for successful maximum-likelihood decoding of the codes.