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

354 PRINCIPLES OF DIGITAL DATA TRANSMISSION
Therefore, a simple detector of duobinary signaling is to first detect all the bits I k corresponding
to b k = ±2. The remaining {bk } are zero-valued samples that imply transition: that is, the
current digit is 1 and the previous digit is 0, or vice versa. This means the digit detection must
be is based on the previous digit. An example of this digit-by-digit detection was shown in
Table 7.1. The disadvantage of the detection method in Eq. (7.43) is that when y(kT b ) = 0, the
current bit decision depends on the previous bit decision. If the previous digit were detected
incorrectly, then the error would tend to propagate, until a sample value of ±2 appears. To
mitigate this error propagation problem, we apply a effective mechanism known as differential
coding.
Figure 7 .18 illustrates a duo binary signal generator by introducing an additional differential
encoder prior to partial-response pulse generation. As shown in Fig. 7.18, differential
encoding is a very simple step that changes the relationship between line code and the message
bits. Differential encoding generates a new binary sequence
modulo 2
with the assumption that the precoder initial state is either po = 0 or po = 1. Now, the precoder
output enters a polar line coder and generates
Because of the duobinary signaling b k = a k + a k - 1 and the zero-1S1 pulse generator, the
samples of the received signal y(t) without noise become
y(kT b ) = bk = a k + a k - 1
= 2(pk + P k - 1) - 2
= 2 (pk- \ EB h + P k - I - 1)
= 1 2(1 - h) P k- I = l
2(h - 1) P k - I = 0
(7.44)
Based on Eq. (7.44), we can summarize the direct relationship between the message bits and
the sample values as
lo h = 1
y( k T b ) =
±2 h = 0
(7.45)
This relationship serves as our basis for a symbol-by-symbol detection algorithm. In short, the
decision algorithm is based on the current sample y(kT b ). When there is no noise, y(kT b ) = b k
and the receiver decision is
2 - ly(kT b )I
h = -- - 2--
(7.46)
Fi g ure 7. 18
Differential
encoded
duobinary
signaling.
Polar
line code