Linear block codes are normally put in systematic form: parity-check part message part Each parity-check bit is a linear sum of message bits,i.e. ，j=0,l.,n-k-1. where p0or 1.Thekequations which gives the parity-check bits are called the parity-check equations.They specify the encoding rule. For an(n.k)block code,the ratios R= and 7=- are called coderate and redundancy,respectively. An example for block code: Let n=7 and k=4.Consider the (7,4)linear systematic block code Message (4,4,2,4） Codeword: (Co,91,C2,C3,C4,C,C6)=(c,9,C2,46,4,4,4) C0=4+41+12 Here, G=4+42+华 C,=t+14+l In matrix form: [1011000] 1110100 c=4,4,4,4i100010 =uG L0110001 Encoder circuit: 3 „ Linear block codes are normally put in systematic form: 01 1 01 01 1 1 (, , ) ( , , , , , ) n nk k parity check part message part cc c − cc c uu u − − − − " =     " " „ Each parity-check bit is a linear sum of message bits, i,e, 1 0 , 0,1, , 1. k j ij i i c pu j n k − = = = −− ∑ " where ij p =0 or 1. The n k − equations which gives the parity-check bits are called the parity-check equations. They specify the encoding rule. „ For an (n, k) block code, the ratios k R n = and n k n η − = are called code rate and redundancy, respectively. „ An example for block code: Let n=7 and k=4. Consider the (7, 4) linear systematic block code Message: 0123 (,) uuuu Codeword: 0123456 012 01 2 3 (,) (, , , ) ccccccc cccuuuu = Here, 0 012 1123 2 013 c uuu cuuu c uuu = ++ =++ = ++ In matrix form: 0123 1 0 11 0 0 0 1 1 10 1 0 0 (,) 1 1 00 0 1 0 0 1 10 0 0 1 uuuu ⎡ ⎤ ⎢ ⎥ = =⋅ ⎣ ⎦ c uG # # # # Encoder circuit: