  Upper and lower bounds on the error probability of linear codes under
maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles
of codes on graphs. For upper bounds, focus is put on Gallager bounding
techniques and their relation to a variety of other reported bounds. Within the
class of lower bounds, we address de Caen's based bounds and their
improvements, sphere-packing bounds, and information-theoretic bounds on the
bit error probability of codes defined on graphs. A comprehensive overview is
provided in a monograph by the authors which is currently in preparation.
