On the threshold of right regular LDPC codes for the erasure channel

We provide an analytical expression for the threshold for right regular low-density parity-check (LDPC) codes for the erasure channel (EC), under message passing decoding. We first develop an expression for the threshold for regular LDPC codes, alternative to that already available in the literature; then we generalize it for the class of right regular codes. Thus, we show that the problem of computing the threshold can be reduced to the search for the fixed points of a function depending only on the variable nodes degree distribution, λ(x), and on the uniform weight, d_c, of check nodes. Finally, we show the application of our analysis to a class of capacity-approaching right regular LDPC codes.