Block codes were the first
parity bits
message bits
k bits
Ex.: (7,4) block code
(0000) (0000000)
(1000) (1101000)
(0100) (0110100)
(1100) (1011100)
(0010) (1110010)
(1010) (0011010)
(0110) (1000110)
(1110) (0101110)
(0001) (1010001)
(1001) (0111001)
(0101) (1100101)
(1101) (0001101)
(0011) (0100011)
(1011) (1001011)
(0111) (0010111)
(1111) (1111111)
(n,k) linear block code
codeword : v = u.G
message
coding :
decoding:
s = r . HT
syndrome
received vector
parity-check matrix
0
no errors,
r = codeword
?0
errors, decoding using syndrome
n-k bits
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