Capacity-achieving sequences for the erasure channel

This paper starts a systematic study of capacity-achieving sequences of low-density parity-check codes for the erasure channel. We introduce a class A of analytic functions, show various useful properties of it, and develop a procedure to obtain degree distributions for the codes. We then study certain types of capacity-achieving sequences and introduce new measures for their optimality. For instance, it turns out that the right-regular sequence is capacity-achieving in a much stronger sense than, e.g., the Tornado sequence