Suppose that a binary source is encoded into $n$ descriptions,
each with rate $1/k$, such that any $k$ descriptions reveal the 
source completely. If fewer than $k$ descriptions are received,
what fraction of the bits can be reproduced if erasures, but
not errors, are permitted? This problem arises in coding for 
peer-to-peer networks and also sheds light on the general 
multiple-descriptions problem.

We prove optimality of a natural scheme modulo a closure 
operation on the rate-distortion region. For small $n$ and
$k$, there is a simple, constructive scheme that is optimal.
Some comments will also be made about distributed encoding.