Signal Space Coding over Rings

Chapter 2: Combined coding and modulation techniques 16
bit error rate, it should be improved for instance by a proper use of convolutional
coding. If a convolutional code of rate 1/2 is used for example, it will require a twice
of the bandwidth to keep the transmission at the same rate with improved error
probability performance. Transmission of 1 bit in a period T can be made using a
modulation like 2PSK. The time diagram and the corresponding constellation are
shown in Fig. 2.2.
Figure 2.2 2PSK transmission and the corresponding constellation
If as a result of the convolutional coding the source bit ‘1’ in Fig. 2.2 produces for
instance a word of two bits, say ‘1 0’, the corresponding time diagram is that of Fig.
2.3.
+1
+1
-1
T sec
T sec
Figure 2.3 4PSK transmission and the corresponding constellation
2PSK
constellation
4PSK
constellation
The bit in Fig 2.2 is encoded by the sequence of Fig. 2.3, which is transmitted over a
higher dimension constellation. As is well known the bandwidth of the 4PSK