Error Probability Bounds for Two Models of Randomized Design of Screening Experiments

The article considers the statement of the problem that arises upon investigating Boolean and linear models of the design of screening experiments. From the standpoint of information theory, this problem is the familiar coding-theory problem of the error probability bounds for two special classes of block codes. Paper [A. G. D'yachkov, Probl. Peredachi Inf., 1979, vol. 15, no. 2, pp. 23–35] obtained upper and lower bounds for the ensemble-mean error probability for such codes for transmission over an arbitrary discrete memoryless channel and maximum-likelihood decoding. In the present paper, the expressions for the exponents of these bounds are investigated for some particular cases of memoryless channels.