## Message doubling and error detection in the binary symmetrical channel.(English)Zbl 1363.94056

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 77-84 (2015).
This article is focused on the problem of error detection in transmission systems (for example security communication in railway interlocking system). Explanation of the concept communication security is described in the paper introduction. Safety codes are an important part of the means of secure communication. The principle of linear binary code is explained in the introduction. It is supposed that a number of message bits are preserved. The adverse communication situation occurs when an undesirable modification of message is realized during its transfer. It means that some bits changed their values during transmission. The problem occurs when the modified message creates key code word different from the sent one. In this case the receiver has no possibility to recognize this critical situation. Described scenario is dangerous because of no detection of created error.
Coding theory is described in the second section, specially stated error detection definition (terms Hamming weight of a word, weight structure of the code). In the following part the problem of probability determining of undetected error is solved. The binary symmetrical channel model and term dual code are defined. The possibilities of calculation of undetected error probability are solved and mathematical relations are derived in this paper. The last chapter solves procedure of use of two independent transmission systems (use of the terms repetition of message, double encoding of the message, weight structure). The received message is accepted only if both copies of message are delivered and are identical (message doubling). Message repetition is an undemanding and at the same time effective method of content protection.
The paper is written clearly and provides a basic overview of secure communication by using of binary symmetrical channel.
For the entire collection see [Zbl 1329.00187].

### MSC:

 94A40 Channel models (including quantum) in information and communication theory 94B70 Error probability in coding theory 62P30 Applications of statistics in engineering and industry; control charts
Full Text: