One-Shot Multivariate Covering Lemmas Via Weighted Sum And Concentration Inequalities

New one-shot bounds for multivariate covering are derived via a weighted sum technique and a one-sided concentration inequality which is stronger than the McDiarmid inequality. The new bounds are more compact and sharper than known bounds in the literature. In particular, the covering error can be shown to decay doubly exponentially in the blocklength. Implications for the error exponent in broadcast channels are discussed.