Encoding process, Computer Networking

Encoding Process

c= uG

u: binary data sequence of length 4( input)

G: Generator matrix which is 7*4

c: Codeword

 

 

797_Encoding Process.png

Decoding Process

s= rHT

r: received data sequence of length 7 ( input) H: Parity-Check Matrix

s: Syndrome to check error-position

 

 

1855_Encoding Process1.png

If some output values of the encoding and decoding multiplication is over than 1, the value should be changed into remainder on division of itself by 2.  (Ex: (4 2 1 ) => (0 0 1))

 

s(Syndrome) detect error position. We can know the single-error-bit position in the table below.

234_Encoding Process2.png

Fig. Decoding table for Hamming code(7,4)

If s is [0 0 0] and r= [0 1 0 0 0 1 1], it supposes that there is no error and transmitted data is [0 0 1 1]. If s is [0 1 0] and r = [1 0 1 0 0 1 0], it supposes that 2th bit is corrupted, so r should be changed to [1 1 1 0 0 1 0], and transmitted data is lower 4bits, [0 0 1 0].

Posted Date: 2/19/2013 1:12:08 AM | Location : United States






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