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The multiterminal secret key agreement problem by public discussion isformulated with an additional source compression step where, prior to thepublic discussion phase, users independently compress their private sources tofilter out strongly correlated components for generating a common secret key.The objective is to maximize the achievable key rate as a function of the jointentropy of the compressed sources. Since the maximum achievable key ratecaptures the total amount of information mutual to the compressed sources, anoptimal compression scheme essentially maximizes the multivariate mutualinformation per bit of randomness of the private sources, and can therefore beviewed more generally as a dimension reduction technique. Single-letter lowerand upper bounds on the maximum achievable key rate are derived for the generalsource model, and an explicit polynomial-time computable formula is obtainedfor the pairwise independent network model. In particular, the converse resultsand the upper bounds are obtained from those of the related secret keyagreement problem with rate-limited discussion. A precise duality is shown forthe two-user case with one-way discussion, and such duality is extended toobtain the desired converse results in the multi-user case. In addition toposing new challenges in information processing and dimension reduction, thecompressed secret key agreement problem helps shed new light on resolving thedifficult problem of secret key agreement with rate-limited discussion, byoffering a more structured achieving scheme and some simpler conjectures toprove.

Compressed Secret Key Agreement: Maximizing Multivariate Mutual Information Per Bit