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A {7, 3, 3} code adds 7 bits to the output stream based on 3 bits of input using a memory of 3 bits. Just as with the CRC codes they use a polynomial to encode the input bits to create the output ...
You can implement FEC techniques for linear block codes (Reed-Solomon codecs) and convolutional codes (Viterbi codecs). To understand this general implementation, look at the hardware behind these ...