Talk abstract:

Constructions of Convolutional Codes with Large Free Distance

Roxana Smarandache
Department of Mathematics
University of Notre Dame
Notre Dame, Indiana 46556
rsmarand@nd.edu

A major parameter of a convolutional code is its free distance d_free since it determines the decoding capability of a code under maximum likelihood decoding. This motivates the search for convolutional codes with a specified rate and degree (or constraint length) that have maximum free distance.

In this talk we present a new bound on the free distance of a convolutional code of a fixed rate k/n and a fixed code degree Since this bound generalizes the Singleton bound for block codes, we call it the generalized Singleton bound. The convolutional codes attaining this bound will be called MDS convolutional codes since they naturally generalize MDS block codes. The goal of the talk is to show how we can construct MDS convolutional codes over fields with prescribed characteristic p. The construction makes use of some techniques developed by Costello, Justesen, Massey and Tanner. Some explicit examples will be provided.

References

[1] J. Justesen. New convolutional code constructions and a class of asymptotically good time-varying codes. IEEE Trans. Inform. Theory, IT-19(2):220-225, 1973.

[2] J.L. Massey, D.J. Costello, and J. Justesen. Polynomial weights and code constructions. IEEE Trans. Inform. Theory, IT-19(1):101-110, 1973.

[3] J. Rosenthal and R. Smarandache. Maximum distance separable convolutional codes. Technical Report 1998-074, MSRI, Berkeley, California, 1998. to appear in Appl. Algebra Engrg. Comm. Comput.

[4] R.M. Tanner. Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes. Computer Research Laboratory, Technical Report, USC-CRL-87-21, November 1987.

Material used used during the talk

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