The rate-distortion function of a binary symmetric source when side information may be absent (Corresp.)

A binary symmetric source with binary side information is given. An encoder codes the source for data compression with no knowledge of the side information. It is then decoded, perhaps with and perhaps without the presence of side information. The rate-distortion function of this scheme is a function of two variables:
D_{1}
is the distortion when side information is present at the decoder, and D2 is the distortion when side information is absent at the decoder. The rate-distortion function is shown to reduce to previously solved problems in much of the
(D_{1}, D_{2})
-plane. Tight upper and lower bounds are found for the rate-distortion function in the rest of the
(D_{1}, D_{2})
-plane.