Exact thresholds for LDPC codes transmitted over binary erasure channels

In this paper we present a simple method for determining the exact decoder convergence thresholds of low-density parity-check codes analytically. We assume transmission over the binary erasure channel and belief propagation decoding. To this aim we use EXIT charts and derive analytical formulas for the EXIT functions of regular and irregular LDPC codes transmitted over the binary erasure channel. Our method is equivalent to density evolution but faster and does not utilize a search algorithm. Thus it is not affected by numerical inaccuracy and does not depend on the number of iterations performed.