Source coding for multiple descriptions II: A binary source

A uniformly distributed (iid) binary source is encoded into two binary data streams at rates R
1
and R
2
, respectively. These sequences are such that by observing either one separately, a decoder can recover a good approximation of the source (at average error rates D
1
, D
2
, respectively), and by observing both sequences, a decoder can obtain a better approximation of the source (at average error rate D
0
). In this paper a “converse” theorem is established on the set of achievable quintuples (R
1
, R
2
, D
0
, D
1
, D
2
). For the special case R
1
= R
2
= 1/2, D
0
= 0, and D
1
= D
2
= D, our result implies that D ≥ 1/5.