Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Christopher Motl01.29.2008Error Correcting Codes•Definitions•Current Uses•Future of Error-correcting codesOverviewCan You Hear Me Now?•Ability to detect errors•Parity bit, Checksum, Cyclic redundancy check, HashingError DetectionError Correction•Ability to detect and correct errors•Automatic repeat request, Error-correcting codeCoding Theory•“a branch of mathematics and computer science dealing with the error-prone process of transmitting data across noisy channels, via clever means, so that a large number of errors that occur can be corrected.”•Two areas of coding theory•Source coding (data compression)•Channel coding (forward error correction)Forward Error Correction•“a system of error control for data transmission, whereby the sender adds redundant data to its messages”•Reduces need to retransmit dataForward Error Correction•Block Coding•Primary type of channel coding used in earlier mobile communication systems.•Convolutional Coding•Often used to improve the performance of digital radio, mobile phones, satellite links, and Bluetooth implementations.Major Uses•Mariner•Voyager•Mars Pathfinder•Mars Exploration Rovers•Cassini ProbeMariner Example•5 bits of data•32 bits transmitted•Up to 7 errors can be correctedCommon Uses•Parchive•High Speed Modems•Barcode - Post Office / UPS•CD / DVD / Hard Drive•Cell Phones•TCP/IP•ISBNTurbo Codes•Most recent development•Combines convolutional codes•Qualcomm EVDO•Deep space satellite communications•What is an Error-correcting code?•What are they used for?•What is in store?RecapHomework1. What is the difference between error detection and error correction?2. What area of mathematics and computer science deals with the transmission of data across noisy
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