Scheduled-PEG construction of LDPC codes for Upper-Layer FEC

TL;DR

This paper introduces a scheduling-optimized PEG algorithm for LDPC code construction, significantly reducing decoding overhead for upper-layer FEC by using genetic algorithms to optimize edge addition order.

Contribution

It formulates and solves an optimization problem for PEG scheduling, leading to LDPC codes with substantially improved decoding performance.

Findings

Optimized scheduling reduces decoding overhead by over 50%.

Genetic algorithms effectively find near-optimal scheduling distributions.

New codes outperform classical PEG codes in erasure correction efficiency.

Abstract

The Progressive Edge Growth (PEG) algorithm is one of the most widely-used method for constructing finite length LDPC codes. In this paper we consider the PEG algorithm together with a scheduling distribution, which specifies the order in which edges are established in the graph. The goal is to find a scheduling distribution that yields "the best" performance in terms of decoding overhead, performance metric specific to erasure codes and widely used for upper-layer forward error correction (UL-FEC). We rigorously formulate this optimization problem, and we show that it can be addressed by using genetic optimization algorithms. We also exhibit PEG codes with optimized scheduling distribution, whose decoding overhead is less than half of the decoding overhead of their classical-PEG counterparts.