Extra Points Reed Solomon Codes Applications

The Reed Solomon Correcting codes have become commonplace in modern digital communications. It was invented in 1960 by Irvin Reed and Gustave Solomon, it helped tecnology providing efficient hardware implementations. It is based in a mathematic area invented by Evariste Galois. 

Some applications that use Reed Solomon Codes nowdays include:

• Storage Devices(HDD,CD,DVD)
• Wireless Comunication(cell-phones,internet)
• Digital Television
• Satellite Communication
• Broadband Modems(ADSL,xDSL)

¿How do they work?

They add extra information to the original data. The encoded data can be stored or transmitted. When trying to recover encoded data they may be some problems with scratches on CDs or some imperfections on HDD surface, detecting the corrupted data for then correcting it depending of the redundancy added.

Real-Life Implementations

There are a number of of-the-shelf Hardware implementations, for instance Advanced Hardware Architectures do a series of VLSI Reed Solomon codecs. Reed Solomon codec could be joined with a convolutional codec (for random error correction), and controlling microprocessor, memory and a transceiver for a complete system-on-a-chip.

More Applications

• Bar Code: This include all 2-dimensional bar codes they all use Reed Solomon correction to allow them a good reading even if a part of the code is damaged. 
• Data Transmission: Specialized forms of Reed–Solomon codes, specifically Cauchy-RS and Vandermonde-RS, can be used to overcome the unreliable nature of data transmission over erasure channels. The encoding process assumes a code of RS(N, K) which results in N codewords of length N symbols each storing K symbols of data, being generated, that are then sent over an erasure channel.
• Satellite Transmissions: Encode digital pictures sent back by the Voyager space probe.

Reference

Joel Sylvester."Reed Solomon Codes."Elektrobit: Web. January 2001.<www.csupomona.edu/~jskang/files/rs1.pdf‎>

Reed–Solomon error correction. (2013, May 2). In Wikipedia, The Free Encyclopedia. Retrieved 16:39, May 9, 2013, from http://en.wikipedia.org/w/index.php title=Reed%E2%80%93Solomon_error_correction&oldid=553215725