Source matching problems revisited

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