Error Exponent Region for Gaussian Broadcast Channels

In this work, we introduce the notion of the error exponent region for a multi-user channel. This region specifies the set of error-exponent vectors that are simultaneously achievable by all users in the multi-user channel. This is done by associating different probabilities of error for different users, contrary to the traditional approach where a single probability of system error is considered. We derive an inner bound (achievable region) and an outer bound for the error exponent region of a Gaussian broadcast channel.