A general formula of rate-distortion functions for source coding with side information at many decoders

Heegard and Berger introduced the model of lossy source coding in which side information is available at many decoders. For this model, their showed an upper bound of the rate-distortion function in the case where the source is stationary memoryless. In this paper, we extend their model to the case where the source may be nonstationary and/or nonergodic, and clarify the rate-distortion function for this model. This result is based on the information-spectrum method introduced by Han and Verdú. We also show some special cases of the rate-distortion function, and a single-letterized upper bound of the rate-distortion function in the case where the source is stationary memoryless.