Sakrison extended Shannon's notion of the rate distortion function to parameterized classes of sources by taking a minimax approach and defining a measure of the minimum rate required for information reconstruction subject to a prescribed fidelity level D. Unfortunately, calculation of Sakrison's rate distortion function may be very difficult because analytic solutions do not generally exist and there has been a lack of a constructive method for finding the rate. However, an approach presented in this correspondence may be used to calculate an approximation to Sakrison's rate distortion function for classes of sources with a finite, discrete input space and a continuous parameter space. The approach gives rise to an algorithm which is shown to be convergent and numerical examples are studied.>

A complete sufficient statistic is presented for the class of all finite-state, finite-order stationary discrete Markov processes. This sufficient statistic is complete in the sense that it summarizes in entirety the whole of the relevant information supplied by any process sample. The sufficient statistic has application to source coding problems such as source matching and calculation of the rate distortion function.>

The source matching problem is to find the minimax codes that minimize the maximum redundancies over classes of sources where relative entropy (cross entropy, discrimination information) is adopted as a criterion to measure the redundancy. The convergence of a simple approach different from L.D. Davisson and A. Leon-Garcia's (1980) algorithm for finding such minimax codes is presented and shown. This approach is applied as an example to the class of first-order discrete Markov sources. The sufficient statistic previously used by D.H. Lee (1983) in his attempt to produce results for the first-order Markov source matching problem is corrected. A computational complexity analysis and a numerical study further demonstrate that this simple algorithm significantly reduces the required computing time, when compared to Davisson and Leon-Garcia's algorithm.>