Digital Signal Processing Reference
In-Depth Information
•
Starting from the state “01” the reception of a “01” leads to the state
“11”. But then both bits would be wrong compared with “10” and the
sum of the correct bits remains “1”. The alternative reception of a “10”
with the transition to the state “10” gives two correct bits, that is on this
path so far 3 correct bits. After two steps this path is the most likely..
• The third bit sequence “10” is now evaluated by means of the state diagram and the
sum of the correct bits registered. Two transitions end in each state point. In state “00”
for example we find two transitions with different sums of the correct bits (3 and 4).
VITERBI decoding is based on deleting the transition with the smaller number of cor-
rect bits as this is the less likely path through the trellis diagram. If the sum of the bits
in the state point is equal in number no path is deleted and both alternatives are pur-
sued further.
• By evaluating the other bit sequences received “01”, “01”, and “11” and constant
deletion of the least likely transitions a “most likely” path in the trellis diagram is
formed.
• The last received bit sequence “00” leads to a decision. The most likely path of the
trellis diagram for the VITERBI decoder is identical to the correct path of the decoder
in the trellis diagram in Illustration 253.
Errors in the sequence received have thus been corrected. By comparing the sum of
the correct bits registered on the right the number of errors which have occurred can be
estimated (14 -12 = 2).
Hard and soft decision
After encoding the signals in the area of the transmitter, modulation follows to make
transmission possible. The signal is demodulated in the receiver. As a result of
interference of the most various kinds during transmission the “0” and “1” states cannot
be as clearly differentiated as in the transmitter.
Apart from interference by noise or other signals the properties of the transmission media
influence the form of signal. In the case of wireless transmission this is for example the
multiple reflection of the transmitted signal by a variety of obstacles which may produce
echo effects or extinguish the signal.
Dispersive characteristics of cable (see Illustration 116) are apparent too. The speed of
transmission in a cable is always frequency-dependent. As a result sinusoidal oscillations
of different frequencies propagate at different speeds which implies a change in the phase
spectrum. This involves a change in the form of the signal.
The signals or bit sequences received are distorted and noisy. If a hard decision is being
used the possibility for the decoder of finding the most likely path in the trellis diagram
is reduced considerably if not completely eliminated. More subtle possibilities of making
decisions should be offered (soft decision).
