1 Developments in iterative decoding

You will recall that the capacity of the binary erasure channel (BEC) with erasure probability p is 1 − p. It was proved [LMSS01] that LDPC codes can achieve the capacity of these channels. In particular, for any � > 0, there exists an infinite family of LDPC codes that have arbitrarily low error probability on the BEC with erasure probability 1 − p − �. To explain how these codes are constructed, I will recall some material from Lecture 13.