  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.
