1. IV. Convolutional Codes

2. Introduction
Block Codes: Code words are produced on a block by block basis.
In Block Codes, the encoder must buffer an entire block before generating the associated codeword.
Some applications have bits arrive serially rather than in large blocks
Convolutional codes operate on the incoming message sequence continuously in a serial manner

3. Convolutional Codes Specification
A convolutional code is specified by three parameters (n, k, K), where
k/n is the coding rate and determines the number of data bits per coded bit
K is called the constraint length of the encoder where the encoder has K-1 memory elements

4. Convolutional Encoder: Example
Rate ½ Convolutional Encoder 1 + c2
Input
Output
1 0 1 c1 + 1

5. Convolutional Encoder: Example
Rate ½ Convolutional Encoder 1 + c2
Input
Output
1 0 1 1
1 1 c1 +

6. Convolutional Encoder: Example
Rate ½ Convolutional Encoder + c2
Input
Output
1 0 1 1 c1 +

7. Convolutional Encoder: Example
Rate ½ Convolutional Encoder + c2
Input
Output
1 0 1 1 c1 +

8. State Diagram Representation
0/00 S0 b0 b1
0/11
1/11
1/00 S2 S1
0/01
States (b0b1)
s0 00
s1 10
s2 01
s3 11
0/10
1/10 S3
1/01
Input 0
Input 1