Mathematician develops more efficient error-correcting codes

Satellites, CD players, modems and mobile phones all depend on being able to deliver clean digital information despite interference…

Satellites, CD players, modems and mobile phones all depend on being able to deliver clean digital information despite interference that can garble messages. These devices use "error-correcting codes" which indicate when a signal has been distorted and help to reinstate it.

A researcher from NUI Maynooth, who already has an error-correcting code named after him, is attempting to develop new codes which work faster and improve the correction rate.

"When you are transmitting digital information from A to B you send a sequence of zeros and ones," explained Dr Gary McGuire, of the department of mathematics at Maynooth. Disturbance or "noise" along the line can change zeros to ones and ones to zeros, he said, "so the message is going to change. There are going to be errors in the message."

The error-correcting codes provide ways to both spot errors and make corrections that bring the signal to its original form. "The trick is to add more zeros and ones to the message so that even if there are errors you can recover the message," Dr McGuire explained.

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The method involves using parts of the original signal to generate a check character. If the original parts and the check don't match up, the code system can regenerate the incorrect part of the signal. This is done on segments of the overall signal, not just once per message so the computations can become very complex, Dr McGuire explained.

"You end up with a mathematical problem," he said, one that is solved using a form of mathematics known as "finite field". The object was to achieve the highest number of messages possible while still being able to handle the resultant potential for errors.

"That is where the mathematical problem comes in," he explained. "The more messages you have the fewer errors you can correct."

Error-correcting codes were being used in the new high-speed modems, he said. CD players use a code known as Reed-Solomon to be able to deliver good sound despite scratches, fingerprints and flaws in the surface of the disc. The space agencies use them to ensure clean data come back from satellite experiments and they are also used with hard-disk drives.

He has already helped to develop one code, the Calderbank-McGuire code, while working with a colleague at Bell Labs in the US. He completed his PhD at the California Institute of Technology before returing to Maynooth to carry out further research into new coding systems.