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The basic idea is that if you send redundant information along with the needed information with any data block (by encoding it using special binary codes) then at the receiver you should be able to detect and correct the error as long as the number of bit errors is less than some limit defined by the the type of the code.
You can read the book "Digital Communications" by Sklar or Proakis. Both have some good material on the subject of error detection and error correction codes.
look you can think about it in the following way we have the data as one's and zero's each one of them represent a piece of information so if we lost any one of them we will actually lost important information.
what if we simply represent each piece of information with more than one bit so that we can use these bits all together or even some of them to reconstruct that piece of information that is what we simply do in FEC.
but actually some times we represent each bit with more than one bit and that is what is called continuous coding as convolutional coding or we divide the data into blocks and then add some redundant bits to that block such as parity check bits an example of that type of coding is such as Reed-Solomon Codes this type of coding is called block coding
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