Talk abstract:

Woven Convolutional Codes: Encoder Properties and Error Exponents

Rolf Johannesson
Department of Information Technology
Information Theory Group
Lund University
P.O. Box 118
SE-221 00 Lund, Sweden
rolf@it.lth.se

Encoders for convolutional codes with large free distances can be constructed by combining several but less powerful convolutional encoders. This paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric. The general construction is called twill and it is described together with two special cases, viz., woven convolutional encoders with outer and inner warp.

The woven convolutional encoders inherit many of their structural properties, such as minimality and catastrophicity, from their constituent encoders.

For all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are presented.

The error exponents and the decoding complexities of binary woven convolutional codes with outer and inner warp are studied. For both constructions, an error probability that is exponentially decreasing with the memory of the woven convolutional codes can be achieved with a non-exponentially increasing decoding complexity. Furthermore, the error exponent for woven convolutional codes with inner warp is larger than the one for woven convolutional codes with outer warp.

The woven convolutional codes are attractive alternatives to the celebrated Turbo codes.

References

[1] R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding, IEEE Press, Piscataway, N.J., Febr., 1999.

[2] S. Höst, R. Johannesson, V.V. Zyablov, "A First Encounter with Woven Convolutional Codes." Proceedings of the 4th International Symposium on Communication Theory and Applications, Lake District, UK, July 13-18, 1997.

[3]S. Höst, R. Johannesson, K. Sh. Zigangirov, and V. V. Zyablov, "Active Distances for Convolutional Codes" IEEE Trans. Inform. Theory, March 1999, pp. 658-669.

[4] S. Höst, R. Johannesson, V.V. Zyablov, and O. Skopintsev, "Generator Matrices of Binary Woven Convolutional Codes," Proceedings of the Sixth Interntional Workshop on "Algebraic and Combinatorial Coding Theory," Pskov, Russia, Sept. 6-12, 1998.

[5] S. Höst, R. Johannesson, O. Skopintsev, and V.V. Zyablov, "Asymptotic Distance Properties of Binary Woven Convolutional Codes." To appear in Problems of Information Transmission.

[6] V. V. Zyablov, S. Shavgulidze, O. Skopintsev, S.Höst, and R. Johannesson, "On the Error Exponent for Woven Convolutional Codes with Outer Warp." To appear in the IEEE Trans. Inform. Theory, July, 1999.

[7] V.V. Zyablov, S. Shavgulidze, and R. Johannesson, "On the Error Exponent for Woven Convolutional Codes with Inner Warp" Submitted to IEEE Trans. Inform. Theory, April 1999.

Material used during the talk

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