An alternate proof of the composite lower bounds

The relations between marginal, joint, and conditional rate-distortion functions are rederived using the Kuhn—Tucker minimization form for the ratedistortion function.. This derivation allows sufficient conditions for the relations to hold with equality to be readily derived. This method is then applied to the rate-distortion function for a stationary source with memory, yielding the composite lower bounds with conditions for equality. The composite lower bounds are also compared to the generalized Wyner—Ziv lower bounds and an example given where the composite lower bounds do better than a comparable generalized Wyner—Ziv bound