A Distance Measure Tailored to Tailbiting Codes

A Distance Measure Tailored to Tailbiting Codes The error-correcting capability of tailbiting codes generated by convolutional encoders is described. In order to obtain a description beyond what the minimum distance d min of the tailbiting code implies, the active tailbiting segment distance is introduced. The description of correctable error patterns via active distances leads to an upper bound on the decoding block error probability of tailbiting codes. The necessary length of a tailbiting code so that its minimum distance is equal to the free distance d free of the convolutional code encoded by the same encoder is easily obtained from the active tailbiting segment distance. This is useful when designing and analyzing concatenated convolutional codes with component codes that are terminated using the tailbiting method. Lower bounds on the active tailbiting segment distance and an upper bound on the ratio between the tailbiting length and memory of the convolutional generator matrix such that d min equals d free are derived. Furthermore, affine lower bounds on the active tailbiting segment distance suggest that good tailbiting codes are generated by convolutional encoders with large active-distance slopes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

A Distance Measure Tailored to Tailbiting Codes

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2002 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1022097828917
Publisher site
See Article on Publisher Site

Abstract

The error-correcting capability of tailbiting codes generated by convolutional encoders is described. In order to obtain a description beyond what the minimum distance d min of the tailbiting code implies, the active tailbiting segment distance is introduced. The description of correctable error patterns via active distances leads to an upper bound on the decoding block error probability of tailbiting codes. The necessary length of a tailbiting code so that its minimum distance is equal to the free distance d free of the convolutional code encoded by the same encoder is easily obtained from the active tailbiting segment distance. This is useful when designing and analyzing concatenated convolutional codes with component codes that are terminated using the tailbiting method. Lower bounds on the active tailbiting segment distance and an upper bound on the ratio between the tailbiting length and memory of the convolutional generator matrix such that d min equals d free are derived. Furthermore, affine lower bounds on the active tailbiting segment distance suggest that good tailbiting codes are generated by convolutional encoders with large active-distance slopes.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 13, 2004

References

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