03-Error Detection and Correction

03-Error Detection and Correction - 1 Error Detection and...

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Unformatted text preview: 1 Error Detection and Correction This week Bit Errors Coding Taxonomy Coding Taxonomy Error Control Coding Parity CRC Codewords / sets Block codes Hamming codes Computer Communications McNair 2011 2 2 Sources of Transmission Errors Thermal noise {Shannon} Impulse noise (e g arcing relays Impulse noise (e..g, arcing relays) Signal distortion during transmission (attenuation) Crosstalk Voice amplitude signal compression (companding) McNair F'11 EEL 5718 Computer Communications 3 Quantization noise (PCM) Jitter (variations in signal timings) Receiver and transmitter out of synch Error Patterns Original Bits (b1,b2, , bn) or Error Vector (e1,e2,,en) Received Pattern = b XOR e (Recall XOR: 1(+)1=0, 1(+)0=1, 0(+)0=0) If ei = 0, no error at bi, if ei = 1, error occurred at bi Random error vectors All possible error patterns are equally likely McNair F'11 EEL 5718 Computer Communications 4 All possible error patterns are equally likely Random bit errors Each bit error occurs independently, with probability p (p = Bit Error Rate, BER) 3 Bit Error Rate (BER) Bit Error BER=10-2 means: On average, 1 out of every 100 bits is an error Burst Errors BER=10-2 could mean: 100 out the first 100 bits are errors, the next 9900 bits are correct McNair F'11 EEL 5718 Computer Communications 5 Typical BER values: Electrical link, BER 10-9 Optical link, BER 10-12 Wireless link, BER 10-2 Example For n=2, what is the probability that there is a one-bit error in a codeword. A) Assume random error patterns (vectors) B) Assume random bit errors McNair F'11 EEL 5718 Computer Communications 6 4 Coding Taxonomy Coding Cryptography (preserve secrecy) (Application Layer) Line Coding (improve spectral characteristics) (Physical Layer) Source Coding (compress data) (Application Layer) Error-control Coding (permit robust transmission of data) (Data Link Layer) McNair F'11 EEL 5718 Computer Communications 7 Error-detection Coding (allow re-transmission of erroneous data) Forward-error-correction (FEC) coding (correct errors even without...
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This note was uploaded on 09/18/2011 for the course EEL 5718 taught by Professor Janisemcnair during the Fall '11 term at University of Florida.

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03-Error Detection and Correction - 1 Error Detection and...

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