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Article

Rychtář, Adam ; Klapka, Štěpán ; Kárná, Lucie
Calculation of the detection properties in the binary symmetrical channel. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 21-26, 2020. Institute of Mathematics CAS, Prague, 2021. pp. 120-128
MSC: 94A40, 94B70 | DOI: 10.21136/panm.2020.12
Keywords:
error correcting codes; error probability; safety codes
Summary:
One of the important parts of railway signalling systems design is the safety of communication, achievable - among others - with the error detecting code. Getting evidence of quantitative safety targets, especially the probability of undetected error of the code, is a surprisingly complicated issue. We've analysed 2048 irreducible self-adjoint generator polynomials of the degree 32. More than 70 of these have a maximum probability of failure lower than the standard codes generally used. In this article we present the best of all codes we've analysed.
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