An iteration method for calculating the relative capacity

An iteration method is given for computing the relative capacity of a discrete memoryless channel, i.e., the maximum of the information transmission rate per cost. The algorithm is simpler and more tractable than that of B. Meister and W. Oettli (1967,Inform. Contr. 11, 341–351). Also it contains Arimoto and Blahut's method for computing the capacity as a special case. The convergence of the iteration method is monotone nondecreasing and a bound on the speed of the convergence is given

A series of identities for the coefficients of inverse matrices on a Hamming scheme

AbstractIn this paper, a series of identities concerned with inverse matrices of a linear combination of association matrices on Hamming schemes is given, which is useful in the field of statistical design of experiments

Combinatorial problems arising from pooling designs for dna library screening

Colbourn (1999) developed some strategy for nonadaptive group testing when the items are linearly ordered and the positive items form a consecutive subset of all items.Müller and Jimbo (2004) improved his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix) requiring that all columns and bitwise OR-sum of each two consecutive columns are pairwise distinct. Such a matrix is called maximal if it has a maximal possible number of columns with respect to some obvious constraints. Using a recursive construction they proved the existence of maximal 2CPD-matrices for any column size m ∈ N except for the case m = 3. Moreover, maximal 2CPD-matrices such that each column is of some fixed constant weight areconstructed. This leads to pooling designs, where each item appears in the same number of pools and all pools are of the same size.Secondly, we investigate 2CPD-matrices of some constant column weight τ ∈ N. We give some recursive construction of such matrices having the maximal possible number of columns. Thirdly, error correction capability of group testing procedures is essential in view of applications such as DNA library screening. We consider a error correcting 2CPD-matrices

Combinatorial aspects of an autonomous system with ternary collisions and of a three person tournament game(New Developments in Statistical Physics Similarities in Diversities,YITP Workshop)

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