text: abstract
  we derive exact (ensemble-tight) error and erasure exponents for the asymmetric broadcast channel given a random superposition codebook. we consider forney’s optimal decoder for both messages and the message pair for the receiver that decodes both
  messages. we prove that the optimal decoder designed to decode the pair of messages achieves the optimal trade-off between the
  total and undetected exponents associated with the optimal decoder for the private message. we propose convex optimization-based
  procedures to evaluate the exponents efficiently. numerical examples are presented to illustrate the results.
  index terms
  broadcast channels, degraded message sets, erasure decoding, undetected error, error exponents, superposition coding.