Multi-user privacy: The Gray-Wyner system and generalized common information

Abstract

The problem of preserving privacy when a multi-variate source is required to be revealed partially to multiple users is modeled as a Gray-Wyner source coding problem with K correlated sources at the encoder and K decoders in which the k th decoder, k = 1, 2, ..., K, losslessly reconstructs the k th source via a common link of rate R 0 and a private link of rate R k . The privacy requirement of keeping each decoder oblivious of all sources other than the one intended for it is introduced via an equivocation constraint E k at decoder k such that the total equivocation summed over all decoders E ≥ Δ. The set of achievable ({R k } K k=1 ,R 0 ,Δ) rates-equivocation (K + 2)-tuples is completely characterized. Using this characterization, two different definitions of common information are presented and are shown to be equivalent.