## Research Abstracts Online

January 2009 - March 2010

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### University of Minnesota Twin Cities

Institute of Technology

Department
of Electrical and Computer Engineering

# PI: John C. Kieffer

### Perturbation Theory of Source Code Design

Convolutional source codes are considered for which the generating matrix consists of two linearly independent binary rows of fixed length such that the first row begins and ends with one; these codes are used to compress a long binary data sequence into a binary sequence half as long. A perturbation class consists of all such codes for which the first row of the generating matrix is the vector of coefficients of a fixed primitive polynomial over the binary field. Each code in the perturbation class is viewed as a nonzero element of the Galois field generated by the primitive polynomial, and lies in a certain conjugacy class. In the perturbation theory of source code design, one selects a code from a perturbation class in two steps: (1) a conjugacy class is selected by a certain rule; (2) a code within that conjugacy class is selected by a certain rule.

These researchers are testing the efficacy of a choice of selection rules (1)-(2). A long pseudorandom binary data sequence is generated, compressed/decompressed via the code in the perturbation class determined by rules (1)-(2), and then the fraction of errors in the decompressed sequence is computed; the primitive polynomial for which this fraction of errors is minimal is then found.

### Group Member

John Marcos, Graduate Student