Rate distortion when side information may be absent

Abstract

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 function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R (D_{l}, D_{2})</tex> is determined where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D_{1}</tex> is the distortion achieved with side information and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D_{2}</tex> is the distortion achieved without it. A generalization is made to the case of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> decoders, each of which is privy to its own side information. An appropriately defined <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> -admissible rate for this general case is shown to equal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R(D)</tex> 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.