  We consider communication over memoryless channels using low-density
parity-check code ensembles above the iterative (belief propagation) threshold.
What is the computational complexity of decoding (i.e., of reconstructing all
the typical input codewords for a given channel output) in this regime? We
define an algorithm accomplishing this task and analyze its typical
performance. The behavior of the new algorithm can be expressed in purely
information-theoretical terms. Its analysis provides an alternative proof of
the area theorem for the binary erasure channel. Finally, we explain how the
area theorem is generalized to arbitrary memoryless channels. We note that the
recently discovered relation between mutual information and minimal square
error is an instance of the area theorem in the setting of Gaussian channels.
