Multiterminal random number generation in of separate coding systems

This paper deals with the random number generation problem in the framework of separate coding system for correlated memoryless sources. L-correlated data sequences with length n are separately encoded to nR _i, i = 1,2,..., L, at each location and those are sent to the information processing center where the encoder wish to generate approximations of nR_L+i bits uniformly distributed random sequence from L-received random messages. Admissible rate region are defined by the set of all the rate vector R^L+1 = (R₁ ,...R_L, R_L+1) for which the approximation error goes to zero as n tends to infinity. In this paper, we examine asymptotic behaviors of the approximation error inside and outside the admissible rate region. We derive an explicit lower bound of the optimal exponent for the approximation error to vanish and show that it can be attained by the universal codes. Furthermore, we derive an explicit lower bound of the optimal exponent for the approximation error to tend to 2 as n goes to infinity outside the admissible rate region. From those results, we can know an explicit form of the admissible rate region