In systematic encoding, just by seeing the output of an encoder, we can separate the data and the redundantīits (also called parity bits). Systematic & Non-systematic encodingīlock codes like Hamming codes are also classified into two categories that differ in terms of structure of the encoder output: The (7,4) binary Hamming block encoder accepts blocks of 4-bit of information, adds 3 parity bits to each such block and produces 7-bits wide Hamming coded blocks. With the simplest configuration: p=3, we get the most basic (7, 4) binary Hamming code. The characteristics of a generic (n,k) Hamming code is given below. All such Hamming codes have a minimum Hamming distance d min=3 and thus they can correct any single bit error and detect any two bit errors in the received vector. Here, 2 p-1 is the number of symbols in the encoded codeword and 2 p-p-1 is the number of information symbols the encoder can accept at a time. For every integer p ≥ 3 (the number of parity bits), there is a (2 p-1, 2 p-p-1) Hamming code. Linear binary Hamming code falls under the category of linear block codes that can correct single bit errors.
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