Rate distortion when side information may be absent

The problem is considered of encoding a discrete memoryless source when correlated side information may or may not be available to the decoder. It is assumed that the side information is not available to the encoder. The rate-distortion functionR (Dₗ, D₂)is determined whereD₁is the distortion achieved with side information andD₂is the distortion achieved without it. A generalization is made to the case ofmdecoders, each of which is privy to its own side information. An appropriately definedD-admissible rate for this general case is shown to equalR(D)when the side information sources satisfy a specified degradedness condition. Explicit results are obtained in the quadratic Gaussian case and in the binary Hamming case.