10-04-2017, 09:03 PM
ERROR CONTROL CODING
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Basic Concepts
Received: 011. What was transmitted?
scenario A: 111 with one error in 1st location
scenario B: 000 with two errors in 2nd & 3rd locations.
Hamming Distance
Def.: The Hamming distance between two codewords ci and cj, denoted by d(ci,cj), is the number of components at which they differ.
Maximum Likelihood Decoding reduces to Minimum Distance Decoding, if the priory probabilities are equal (P(0)=P(1))
Error Correction and Detection
Consider a code consisting of two codewords with Hamming distance dmin. How many errors can be detected? Corrected?