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Convolutional codes are one type of code used for channel coding . Another type of code used is block coding .
In convolutional codes, each block of bits is mapped into a block of bits but these bits are not only determined by the present information bits but also by the previous information bits. Thisdependence can be captured by a finite state machine.
A rate convolutional coder , with memory length 2 and constraint length 3.
Since the length of the shift register is 2, there are 4
different rates. The behavior of the convolutional codercan be captured by a 4 state machine. States:
00,
01, 10, 11 ,
For example, arrival of information bit
0 transitions from state
10 to state
01 .
The encoding and the decoding process can be realized in trellis structure.
If the input sequence is
1 1 0 0
the output sequence would be
11 10 10 11
The transmitted codeword is then
11 10 10
11 . If there is one error on the channel
11
0 0 10 11
Starting from state
00 the Hamming
distance between the possible paths and the receivedsequence is measured. At the end, the path with minimum
distance to the received sequence is chosen as the correcttrellis path. The information sequence will then be
determined.
Convolutional coding lends itself to very efficient trellis based encoding and decoding. They are very practical andpowerful codes.
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