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Question 2 ( 7 0 pts ) In Matlab, the trellis diagram for the 1 st row of Table 7 . 4 ( Constraint Length,

Question 2(70 pts)
In Matlab, the trellis diagram for the 1 st row of Table 7.4(Constraint Length, K=3 and rate 12 code)
can be stated as follows,
trellis = poly2trellis (3,{'1+x+x???2',?'1+x???2'})
a)(10 pts) Plot the simulated BER for the coded BPSK system for rate 12 convolutionally code
with constraint lengths K=3,K=5 and K=7 respectively. You can generate 5 Million
information bits, EbN0 varies between 2dB to 8dB, and set the zero mean Gaussian channel
noise variance is 1.
b)(20 pts) For Hard decision decoding (HDD), plot the coded BER for each value of K and its
BER upperbound. You can use "bercoding" command to compute the coded BER
upperbound. For a given EbN0, is it a good idea to use the BER upperbound when the simulated
BER is not available? Comment on your results. To compute the upperbound, you can use
"distspec(trellis,10)".
c)(10 pts) Plot execution time of the Viterbi decoder for 5 million information bits for each
value of K given in Q2, part (a). Hint: You can use tic, toc commands or see etime function.
d)(30 pts) Now you should seek the performance of soft decision decoding (SDD) instead of
HDD. You should partition the interval between -1 and +1 into L intervals.
As an example, for L=4, you can set the decision thresholds as -0.500.5 or for L=8, you
can set the decision thresholds as [-0.75-0.5-0.2500.250.50.75 and so on. Let si be a soft
decision 2 bit (L=4 level) sample, then si is obtained from the received coded BPSK symbol
ri from,
si={0,ri-0.51,-0.50.5
To obtain the quantized soft decisions from the received coded BPSK symbolds, you can use
the function "quantiz". Then, for a rate 12 convolutional code with K=3, obtain the BER and
BER upperbound for SDD. Also compare your results with BER and its upperbound for HDD.
Comment on your results.
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