Binary erasure multiple descriptions: Average-case distortion

We consider a binary erasure version of the n-channel multiple descriptions problem with no excess rate and no distortion for every k out of n descriptions, i.e., any subset of k messages has a total rate of one and allows for perfect reconstruction of the source. We present an achievability scheme and characterize its distortion when m < k messages are received at the decoder. We show that the scheme is optimal for the case where (1 - 1/n)^k les 1/2 and a single message is received. For the case where k = 2, n > 3 and a single message is received, we provide a lower bound that differs by exactly 1/n from the minimum distortion achieved by the scheme.