B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

432 FUNDAMENTALS OF PROBABILITY THEORY
Figure 8.16
(a) Quantization
error in PCM
and (b) its PDF.
I
m(t) t
2mµIL
m/L q -
(b)
as shown in Fig. 8.16b, and
=
q
3
2mp 3
=Cif
/L
lmµ-mµ /L
From Fig. 8.16b it can be seen that q = 0. Hence,
(8.68a)
(8.68b)
Example 8.21 Mean Square Error Caused by Channel Noise in PCM
Quantization noise is one of the sources of error in PCM. The other source of error is channel
noise. Each quantized sample is coded by a group of n binary pulses. Because of channel noise,
some of these pulses are incorrectly detected atthe receiver. Hence, the decoded sample value
m at the receiver will differ from the quantized sample value ID that is transmitted. The error
E = ID - mis a random variable. Let us calculate E 2 , the mean square error in the sample value
caused by the channel noise.