Abstract
In this contribution, the probability of undetected errors on channels with memory is determined. Different error detection strategies (e.g. shortened hamming codes), which have been adopted as international standards, were analyzed. A setup is presented, which is based on a classification of error patterns in blocks by error-length and errorweight. This approach is used to determine the probability of an error pattern being a valid codeword and consequently not detectable. For these investigations a digital channel model, whose characteristics were found by analyzing real shortwave channel connections, was used. As a result of the investigation it is shown, that generator polynomials of the same code rate on channels with memory are the more efficiently the more equidistantly the exponents in the generator polynomial are distributed.
This contribution was presented in parts at the Nordic HF Conference, Fårö/Sweden, August 2001.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahrens, A., Wilhelm, C.: Bestimmung des Reduktionsfaktors bei Einsatz zyklischer Codes auf Kanälen mit gebündelt auftretenden Übertragungsfehlern. 10. Symposium Maritime Elektronik, Arbeitskreis Maritime Mess-und Informationselektronik, June 2001, Universität Rostock, Germany, (141–144)
Ahrens, A., Lange, C.: On the Probability of Undetected Error in Protocol Structures. Nordic Shortwave Conference (Nordic HF 01), August2001, Fårö, Sweden, (3.1.1–3.1.8)
Ahrens, A.: A New Digital Channel Model Suitable for the Simulation and Evaluation of Channel Error Effects. Colloquium on Speech Coding Algorithms for Radio Channels, IEE Electronics and Communications, April 2000, London, UK, Reference Number 2000/030
Ahrens, A., Greiner, G.: A Radio Protocol for TCP/IP Application. Colloquium on Frequency Selection and Management Techniques for HF Communication, IEE Electronics and Communications, March 1999, London, UK, Reference Number 1999/017, 11/1-11/6
Fujiwara, T., Kasami, T.; Kitai, A., Lin, S.: On the Undetected Error Probability for Shortened Hamming Codes. IEEE Transactions on Communications 33 (1985) 570–574
Leung, C.: Evaluation of the Undetected Error Probability of Single Parity-Check Product Codes. IEEE Transactions on Communications 31 (1983) 250–253
Wilhelm, C.: Über den Zusammenhang zwischen Kanal und Codierung bei der Datenfernübertragung. Nachrichtentechnik-Elektronik 17 (1967) 386–392
Wilhelm, C.: Datenübertragung. Militärverlag, Berlin (1976)
Wozencraft, J. M., Jacobs, I. M.: Principles of Communication Engineering. Waveland Press, Prospect Heigths (Illinios) (1990)
Wolf, J., Michelson, A., Levesque, A.: On the Probability of Undetected Error for Linear Block Codes. IEEE Transactions on Communications 30 (1982) 317–324
Wong, B., Leung, C.: On Computing Undetected Error Probabilities on the Gilbert Channel. IEEE Transactions on Communications 43 (1995) 2657–2661
Witzke, B., Leung, C.: A Comparison of some Error Detecting CRC Code Standards. IEEE Transactions on Communications 33 (1985) 996–998
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lange, C., Ahrens, A. (2001). On the Undetected Error Probability for Shortened Hamming Codes on Channels with Memory. In: Honary, B. (eds) Cryptography and Coding. Cryptography and Coding 2001. Lecture Notes in Computer Science, vol 2260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45325-3_2
Download citation
DOI: https://doi.org/10.1007/3-540-45325-3_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43026-1
Online ISBN: 978-3-540-45325-3
eBook Packages: Springer Book Archive