Capacity-Achieving Sequences

Abstract

A capacity-achieving sequence of degree distributions for the erasurechannel is, roughly speaking, a sequence of degree distributionssuch that graphs sampled uniformly at random satisfying those degreeconstraints lead to codes that perform arbitrarily close to the capacityof the erasure channel when decoded with a simple erasure decoderdescribed in the paper. We will prove a necessary property calledflatness for a sequence of degree distributions to be capacity-achieving,and will comment on possible applications to the design of capacity-achievingsequences on other communication channels.