In convolutional codes, each block of

### Example 1

A rate

Since the length of the shift register is 2, there are 4
different rates. The behavior of the convolutional coder
can 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 received
sequence is measured. At the end, the path with minimum
distance to the received sequence is chosen as the correct
trellis path. The information sequence will then be
determined.

Convolutional coding lends itself to very efficient trellis based encoding and decoding. They are very practical and powerful codes.