ASSIGNMENT #1

DIGITAL COMMUNIATION

(Line Coding)

Q1. Find PSDs for polar, on-off, and bipolar signaling, for a full-width rectangular pulse, p(t) = rect (t/Tb),

where Tb is bit period. Sketch roughly these PSDs and find their bandwidths. For each case, compare

the bandwidth to the case where p(t) is a half-width rectangular pulse.

Q2. A random binary sequence 100110 is transmitted using a Manchester (split-phase) line code. Sketch

the waveform y(t). Derive Sy(), assuming 1 and 0 equally likely. Sketch this PSD and find its bandwidth.

Q3. Derive the PSD for a binary signal using differential code with half-width rectangular pulses.

Q4. A 3 kHz bandwidth channel is used to transmit binary data. Calculate the data rate (in bps) that can be

transmitted if we use: {Unipolar, Polar, and Bipolar} (NRZ & RZ) and Manchester signalling.

Q5. For a rectangular pulse p(t) of amplitude A, find the average power required to transmit one bit using,

Unipolar NRZ & RZ, Polar NRZ & RZ, Bipolar NRZ & RZ; and Manchester signalling, in terms of

amplitude A. Find the value of A for average power equal to unity, in each case.

Q6. The duobinary line coding proposed by Lender is also ternary like bipolar, but requires only half the

bandwidth of bipolar. In practice, duobinary coding is indirectly realized using a special pulse shape. In

this code, a 0 is transmitted by no pulse, and a 1 is transmitted by a pulse p(t) or -p(t) using the following

rule. A 1 is encoded by the same pulse as that used for the previous 1, if there is an even number of 0s

between them. It is encoded by a pulse of opposite polarity if there is an odd number of 0s between them.

Like bipolar, this code also has a single error detection capability, because correct reception implies that

between successive pulses of the same polarity, an even number of 0s must occur, and between

successive pulses of opposite polarity, an odd number of 0s must occur.

a) Using a half-width pulse p(t), sketch the duobinary signal y(t) for the random binary sequence

1110001101001010

b) Determine R0, R1 and R2 for this code. Assume (or, prove if you like) that Rn = 0 for all n > 2. Find

and sketch the PSD for this line code (assuming half-width pulse). Show that its bandwidth is Rb/2

Hz, half that of bipolar.

c) In a binary data transmission using duobinary pulses, sample values of the received pulses were:-

2 0 -2 -2 0 0 -2 0 2 0 0 2 0 0 0 -2

Is there any error in detection? If there is no detection error, determine the received bit sequence.

d) In a binary data transmission using duobinary pulses, sample values of the received pulses were:-

2 0 0 0 -2 0 0 -2 0 2 0 0 -2 0 2 2 0 -2

Is there any error in detection? Can you guess the correct transmitted digit sequence? There is

more than one possible correct sequence. Give as many as possible correct sequences, assuming

that more than one detection error is extremely unlikely.