An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are ‘-1’, ‘0’ and ‘1’.

The values of a and b are

During transmission over a certain binary communication channel, bit errors occurs independently with probability p. The probability of at most one bit in error in a block of n bits is given by

In a Direct sequence CDMA system the chip rate is $$1.2288\,\, \times \,\,{10^6}$$ chips per second. If the processing gain is desired to be at least 100. The data rate

The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$$p(t) = {{\sin \,4\,\pi \,W\,t} \over \matrix{ 4\,\pi \,W\,t(1 - 16{W^2}{t^2}) \hfill \cr \hfill \cr \hfill \cr} }$$$ The value of p(t) at $$t = {1 \over {4\,W}}$$ is