Remark on “Toom’s partial order is transitive” published in Probl. Peredachi Inf., 2012, no. 2

Remark on “Toom’s partial order is transitive” published in Probl. Peredachi Inf., 2012, no. 2 ISSN 0032-9460, Problems of Information Transmission, 2014, Vol. 50, No. 3, pp. 292–301.  c Pleiades Publishing, Inc., 2014. Original Russian Text  c M.A. Raskin, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 3, pp. 101–111. LETTERS TO THE EDITOR Remark on “Toom’s Partial Order Is Transitive” Published in Probl. Peredachi Inf., 2012, no. 2 M. A. Raskin DOI: 10.1134/S0032946014030089 In my paper “Toom’s Partial Order Is Transitive” (Probl. Peredachi Inf., 2012, vol. 48, no. 2, pp. 79–99) there is a mistake in the proof of Theorem 3. In the construction given in the paper for the proof of additivity of the constructed measures α and β , we assume that the distributions of zeros inserted into a given word y with respect to the measures α and β can be taken to be independent. This assumption does not take into account the fact that the distribution of the number of zeros and the distribution of the succeeding nonzero symbol may be dependent. For example, Y -projection of the measure α may consist of independently chosen equiprobable blocks ⊕⊕ and ⊕⊕⊕. This mistake can be corrected by using averaging and considering the accumulation point of the Problems of Information Transmission Springer Journals

Remark on “Toom’s partial order is transitive” published in Probl. Peredachi Inf., 2012, no. 2

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Pleiades Publishing
Copyright © 2014 by Pleiades Publishing, Inc.
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
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