On multiple descriptions and team guessing

Witsenhausen\´s hyperbola bound for the multiple description problem without excess rate in case of a binary source is not tight for exact joint reproductions. However, this bound is tight for almost-exact joint reproductions (Theorem , conjectured by Witsenhausen). The proof is based on an {em approximative} form of the team guessing lemma for {em sequences} of random variables. (This result may be of interest also for team guessing). The hyperbola bound is also tight for exact joint reproductions and arbitrarily small, but positive, excess rate (Theorem . The proof of this result uses our covering lemma.