Waveform Encoding - Digital Communication: Principles and System Modelling - page 35

d i

^
d i

Z

i

∑

∑

Quantizer

Z i

-

Delay

^
Z i

Z i −1

Transmitter Receiver

Fig. 2.20 Basic DPCM communication system

= d 1 + Z 0 (As at 0th instant Z 0 = Z 0 )

And the quantized difference

d i =

d i + e q i (2.26)

So, from the diagram presented in Fig. 2.20 ,

Z 1 = d 1 + e q 1 + Z 0

(2.27)

Or Z 1 = Z 1 + e q 1

Now, for i = 2, we get from Eq. ( 2.25 ),

Z 2 = d 2 + Z 1

(2.28)

Z 2 = d 2 + e q 2 + Z 1 + e q 1

Z 2 = Z 2 + e q 1 + e q 2

Proceeding in this way we can see

n

Z n = Z n + e q i (2.29)

i = 1

So, here we see that in case of basic configuration of DPCM, the output at n th instant
is affected not only by the quantization error of n th instant, but also by the errors
of previous instants. The error becomes severe as the term of samples increases. To
overcome the problem, a new configuration is designed.

2.3.2 Prevention of Cumulative Error by Applying Feedback

In the receiver section, a delay feedback path is used for proper recovery of the
message sample. To solve the problem of cumulative quantization error in the trans-
mitted samples, we have just copied the feedback loop of the receiver section and
pasted to the transmitter section as shown in Fig. 2.21 .