Talk abstract:

Multidimensional Convolutional Codes

Paul A. Weiner
Saint Mary's University of Minnesota
pweiner@smumn.edu

Multidimensional convolutional codes are the higher dimensional generalizations of (one-dimensional) convolutional codes. They allow for error detection and correction in the transmission of higher dimensional data (e.g., 2-D-pictures; 3-D-animation, holograms; 4-D-animated holograms). We will concentrate on the mathematical description and properties of these codes.

Let F=F_q be the finite field with q elements, and let R=F[z₁, z₁, ..., z_m] be the polynomial ring in m indeterminates over F. An m-dimensional convolutional code of length n may be defined to be an R-submodule of the free module Rⁿ. Multidimensional convolutional codes then are a nontrivial generalization of (1-dimensional) convolutional codes-there are significant structural differences in higher dimensional codes, due to the increased complexity of the corresponding polynomial rings.

We will consider basic definitions and properties of m-dimensional convolutional codes, including generator matrices, free and nonfree codes, encoders for free codes, and distance of a code.

We will also give a code construction for which there is a lower distance bound.

Material used during the talk

Back to Codes, Systems and Graphical Models

1998-1999 Mathematics in Biology