PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov, Flossie Dunlop.

Title:A new approach to CRC processing
Seminar:MASS Colloquium
Speaker:Donald Newhart, NSA
Abstract:
High-speed digital communications must anticipate the possibility of channel errors in transmission. Nontrivial mathematical approaches to this date back to 1948, and constitute the subject of Algebraic Coding Theory. The principle of using the coefficients of polynomial remainders as a checksum to detect errors goes back to at least 1961; this idea blended well with the technology of shift registers, and is used in everything from the GPS system to the internet. Advances in modern technology such as Field Programmable Gate Arrays (FPGA), allows for very efficient vector addition of long binary inputs, and open new possibilities. This talk will explain CRC checksums from first principles, show how abstract algebra plays a pivotal role, and finally, present a new mathematical algorithm (developed at NSA) to process them. Although the approach will be explained with some simple linear algebra, it implicitly takes advantage of an underlying quotient-ring context that is usually ignored. Potential advantages for FPGA use will be discussed.

Room Reservation Information

Room Number:MB113
Date:10 / 04 / 2012
Time:02:30pm - 03:30pm