Unit-2

Digital Communication Basics

The elements which form a digital communication system is represented by the following block diagram for the ease of understanding.

Following are the sections of the digital communication system.

Source

The source can be an analog signal.

Example: A Sound signal

Input Transducer

This is a transducer which takes a physical input and converts it to an electrical signal. This block also consists of an analog to digital converter where a digital signal is needed for further processes.

A digital signal is generally represented by a binary sequence.

Source Encoder

The source encoder compresses the data into minimum number of bits. This process helps in effective utilization of the bandwidth. It removes the redundant bits unnecessary excess bits, i.e. ,zeroes.

Channel Encoder

The channel encoder, does the coding for error correction. During the transmission of the signal, due to the noise in the channel, the signal may get altered and hence to avoid this, the channel encoder adds some redundant bits to the transmitted data. These are the error correcting bits.

Digital Modulator

The signal to be transmitted is modulated here by a carrier. The signal is also converted to analog from the digital sequence, in order to make it travel through the channel or medium.

Channel

The channel or a medium, allows the analog signal to transmit from the transmitter end to the receiver end.

Digital Demodulator

This is the first step at the receiver end. The received signal is demodulated as well as converted again from analog to digital. The signal gets reconstructed here.

Channel Decoder

The channel decoder, after detecting the sequence, does some error corrections. The distortions which might occur during the transmission, are corrected by adding some redundant bits. This addition of bits helps in the complete recovery of the original signal.

Source Decoder

The resultant signal is once again digitized by sampling and quantizing so that the pure digital output is obtained without the loss of information. The source decoder recreates the source output.

Output Transducer

This is the last block which converts the signal into the original physical form, which was at the input of the transmitter. It converts the electrical signal into physical output.

Output Signal

This is the output which is produced after the whole process.

A line code is the code used for data transmission of a digital signal over a transmission line. This process of coding is chosen so as to avoid overlap and distortion of signal such as inter-symbol interference.

Properties of Line Coding

Following are the properties of line coding −

Types of Line Coding

There are 3 types of Line Coding

Unipolar Signaling

Unipolar signaling is also called as On-Off Keying or simply OOK.

The presence of pulse represents a 1 and the absence of pulse represents a 0.

There are two variations in Unipolar signaling −

Unipolar Non-Return to Zero NRZ

In this type of unipolar signaling, a High in data is represented by a positive pulse called as Mark, which has a duration T0 equal to the symbol bit duration. A Low in data input has no pulse.

The following figure clearly depicts this.

Advantages

The advantages of Unipolar NRZ are −

Disadvantages

The disadvantages of Unipolar NRZ are −

Unipolar Return to Zero RZRZ

In this type of unipolar signaling, a High in data, though represented by a Mark pulse, its duration T0 is less than the symbol bit duration. Half of the bit duration remains high but it immediately returns to zero and shows the absence of pulse during the remaining half of the bit duration.

It is clearly understood with the help of the following figure.

Advantages

The advantages of Unipolar RZ are −

Disadvantages

The disadvantages of Unipolar RZ are −

Polar Signaling

There are two methods of Polar Signaling. They are −

Polar NRZ

In this type of Polar signaling, a High in data is represented by a positive pulse, while a Low in data is represented by a negative pulse. The following figure depicts this well.

Advantages

The advantages of Polar NRZ are −

Disadvantages

The disadvantages of Polar NRZ are −

Polar RZ

In this type of Polar signaling, a High in data, though represented by a Mark pulse, its duration T0 is less than the symbol bit duration. Half of the bit duration remains high but it immediately returns to zero and shows the absence of pulse during the remaining half of the bit duration.

However, for a Low input, a negative pulse represents the data, and the zero level remains same for the other half of the bit duration. The following figure depicts this clearly.

Advantages

The advantages of Polar RZ are −

Disadvantages

The disadvantages of Polar RZ are −

Bipolar Signaling

This is an encoding technique which has three voltage levels namely +, - and 0. Such a signal is called as duo-binary signal.

An example of this type is Alternate Mark Inversion AMIAMI. For a 1, the voltage level gets a transition from + to – or from – to +, having alternate 1s to be of equal polarity. A 0 will have a zero voltage level.

Even in this method, we have two types.

From the models so far discussed, we have learnt the difference between NRZ and RZ. It just goes in the same way here too. The following figure clearly depicts this.

The above figure has both the Bipolar NRZ and RZ waveforms. The pulse duration and symbol bit duration are equal in NRZ type, while the pulse duration is half of the symbol bit duration in RZ type.

Advantages

Following are the advantages −

Disadvantages

Following are the disadvantages −

Power Spectral Density

The function which describes how the power of a signal got distributed at various frequencies, in the frequency domain is called as Power Spectral Density PSD.

PSD is the Fourier Transform of Auto-Correlation Similarity between observations. It is in the form of a rectangular pulse.

The scrambling can mean many things when it comes to digital signal processing.

Here are some uses.

1. Energy dispersal - to redistribute bits when there may be too many zeros or 1’s are in a row.

2. Forward error correction - In order code data so random errors can be corrected, the data may be reordered either using convolutional or some other type of coding.

3. Burst error protection - Data may be scrambled to protect it from burst errors. This is done by interleaving, which can be row to column or use convolution.

4. Encryption - We would not use the term scrambling per say to encrypt a data sequence because a specific algorithm is being used, it is scrambling in common sense.

5. Code division multiplexing - A pseudo-random sequence is multiplied with a data sequence and hence results in a much bigger scrambled sequence.

An eye diagram or eye pattern is simply a graphical display of a serial data signal with respect to time that shows a pattern that resembles an eye.

The signal at the receiving end of the serial link is connected to an oscilloscope and the sweep rate is set so that one- or two-bit time periods (unit intervals or UI) are displayed. This causes bit periods to overlap and the eye pattern to form around the upper and lower signal levels and the rise and fall times. The eye pattern readily shows the rise and fall time lengthening and rounding as well as the horizontal jitter variation.

This algorithm makes it possible to construct, for each list of linearly independent vectors (resp. basis), a corresponding orthonormal list (resp. orthonormal basis).

If (v1,…,vm) is a list of linearly independent vectors in VV, then there exists an orthonormal list (e1,…,em) such that

span(v1,…,vk)=span(e1,…,ek),for all k=1,…,m.

The proof is constructive, that is, we will actually construct vectors e1,…,em having the desired properties.

Since (v1,…,vm) is linearly independent, vk≠0for each k=1,2,…,m. Set e1=v1∥v1∥. Then e1 is a vector of norm 1 and satisfies Equation for k=1. Next, set

e2=v2−⟨v2, e1⟩e1∥v2−⟨v2, e1⟩e1∥.

This is, in fact, the normalized version of the orthogonal decomposition I.e.,

w=v2−⟨v2, e1⟩e1,

where w⊥e1. Note that ∥e2∥=1 and span(e1, e2)=span(v1,v2).

Now, suppose that e1,…,ek−1 have been constructed such that (e1,…,ek−1) is an orthonormal list and span(v1,…,vk−1)=span(e1,…,ek−1). Then define

ek=vk−⟨vk,e1⟩e1−⟨vk,e2⟩e2−⋯−⟨vk,ek−1⟩ek−1∥vk−⟨vk,e1⟩e1−⟨vk,e2⟩e2−⋯−⟨vk,ek−1⟩ek−1∥.

Since (v1,…,vk) is linearly independent, we know that vk∉span (v1,…,vk−1). Hence, we also know that vk∉span (e1,…,ek−1). It follows that the norm in the definition of ek is not zero, and so ek is well-defined (i.e., we are not dividing by zero). Note that a vector divided by its norm has norm 1 so that ∥ek∥=1. Furthermore,

⟨ek,ei⟩=⟨vk−⟨vk,e1⟩e1−⟨vk,e2⟩e2−⋯−⟨vk,ek−1⟩ek−1∥vk−⟨vk,e1⟩e1−⟨vk,e2⟩e2−⋯−⟨vk,ek−1⟩ek−1∥,ei⟩=⟨vk,ei⟩−⟨vk,ei⟩∥vk−⟨vk,e1⟩e1−⟨vk,e2⟩e2−⋯−⟨vk,ek−1⟩ek−1∥=0,

for each 1≤i<k. Hence, (e1,…,ek) is orthonormal.

Reference:

1. P Ramkrishna Rao, Digital Communication, McGraw Hill Publication

2. Ha Nguyen, Ed Shwedyk, ―A First Course in Digital Communication‖, Cambridge

University Press.

3. B P Lathi, Zhi Ding ―Modern Analog and Digital Communication System‖, Oxford

University Press, Fourth Edition.

4. Bernard Sklar, Prabitra Kumar Ray, ―Digital Communications Fundamentals and

Applications‖ Second Edition, Pearson Education

5. Taub, Schilling, ―Principles of Communication System‖, Fourth Edition, McGraw Hill.