Today's lecture discussed convolutional codes, which differ from block codes in that they encode entire data streams continuously rather than segmenting data into blocks. Convolutional codes can be represented using vectors, impulse responses, polynomials, state diagrams, and trellis diagrams. A rate 1/2 convolutional code with constraint length K=3 was used as a example. The encoder for this code was explained and its state diagram and trellis representation were shown.

1. Modulation, Demodulation and Coding Course Period 3 - 2005 Sorour Falahati Lecture 9

7. A Rate ½ Convolutional encoder Time Output Output Time Message sequence: (Branch word) (Branch word) 1 0 0 0 1 0 1 0 1 0 1 0

8. A Rate ½ Convolutional encoder Encoder 0 0 1 0 0 0 Time Output Time Output (Branch word) (Branch word)

16. State diagram – cont’d 10 01 00 11 1/11 1/00 1/01 1/10 0/11 0/00 0/01 0/10 Input Output (Branch word) output Next state input Current state 10 1 01 0 11 01 1 10 0 10 00 1 11 0 01 11 1 00 0 00

19. Trellis – cont’d 1/11 0/00 0/10 1/11 1/01 0/00 0/11 0/10 0/01 0/00 0/11 0/00 Input bits Output bits Tail bits 0/11 0/10 0/01 1/11 1/01 1/00 0/00 1 0 1 0 0 11 10 00 10 11