  Error and erasure exponents for the broadcast channel with degraded message
sets are analyzed. The focus of our error probability analysis is on the main
receiver where, nominally, both messages are to be decoded. A two-step decoding
algorithm is proposed and analyzed. This receiver first attempts to decode both
messages, failing which, it attempts to decode only the message representing
the coarser information, i.e., the cloud center. This algorithm reflects the
intuition that we should decode both messages only if we have confidence in the
estimates; otherwise one should only decode the coarser information. The
resulting error and erasure exponents, derived using the method of types, are
expressed in terms of a penalized form of the modified random coding error
exponent.
