# Source coding and Channel coding

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Source coding and Channel coding
Wireless Systems Source coding and Channel coding

Block Diagram of a Digital System

Digital Transmission What is Digital Transmission?
A computer network is designed to send information from one point to another. This information needs to be converted either to digital signal or analog signal for transmission. Why Digital Signals are better than Analog Signals?

Digital to Digital Conversion
In previous lectures you have come to know what is the difference between a data and signal. We said that data can be either digital or analog. Here we will see how we can represent digital data by using digital signals. The conversion involves three techniques: Line Coding, Block Coding and Scrambling. Line Coding is always needed, Block Coding and scrambling may not be needed.

Line Coding Line Coding is the process of converting Digital Data to Digital Signals. We assume data can be in the form of text, numbers, graphical images, audio or video are stored in the computer memory as sequences of bits. You know computer is a Digital Device so data is always in the form of binary (0,1) Line Coding converts a sequence of bits to a Digital Signal. At the Sender Digital data are encoded into a Digital Signal. So at the receiver you need to decode the signal to retrieve the digital data.

Characteristics Before discussing different line coding schemes, we will address their common characteristic and their common characteristic will be?

Signal Element Versus Data Element
Let us distinguish between a signal element and a data element. In data communications, our goal is to send data elements. A data element is the smallest entity that can represent a piece of information: this is the bit. In digital data communications, a signal element carries data elements. A signal element is the shortest unit (time wise) of a digital signal.

Signal Element Versus Data Element (Continued)
In other words, data elements are what we need to send: signal elements are what we can send. Data elements are being carried; signal elements are the carrier. We define a ratio r which is the number of data elements carried by each signal element. Figure on the next page will highlight several situations with different values of r.

Signal Element Verses Data Element

Explanation In part a of the figure, one data element is carried by one signal element so r=1. In part b of the figure, we need 2 signal elements to carry each data element (r=1/2). We will see later why extra signal element is needed to guarantee synchronization. In part c of the figure a signal element carries 2 data elements so r=2 and finally r= 4/3. For every line coding schemes we discuss, will give the value of r.

Explanation (Continued)
An analogy may help here. Suppose each data element is a person who need to be carried from one place to another. We can think of a signal element as a vehicle that can carry people. When r=1 means each person is driving a vehicle. Where r>1 means that more persons are traveling in the vehicle. Do you have a clear understanding now? It is not difficult. Easiest way to tackle it is keep things simple and straightforward.

Data Rate Versus Signal Rate
The data rate defines the number of data elements (bits) sent in 1 second. The unit is bits per second (bps) The signal rate is the number of signal elements sent in 1 second. The unit is baud. The data rate is sometimes called the bit rate, and the signal rate is sometimes called a pulse rate, the modulation rate or the baud rate. Our goal in data communication is to increase the data rate while decreasing the signal rate. Increasing the data rate will increase the speed of transmission, decreasing the signal rate decreases the bandwidth requirement.

Discussion (Continued)
We now need to consider the relationship between the data rate and signal rate. The relationship, of course depends on the value of r. It also depends on the data pattern. If we have the pattern of all 1’s and 0’s the signal rate may be different from a data pattern of alternating 0’s and 1’s. To establish a mathematical formula we need to define three cases. The worst, best and average. The worst case is when we need max signal rate and the best case is when we need the minimum.

Relationship between data rate and signal rate
The formula is s= c x N x 1/ r Where N is the data rate, bps c is the case factor that varies for each case, s is the number of signal elements, and r is the previously defined factor. Example: A signal is carrying data in which one data element is encoded as one signal element. If the bit rate is 100kbps, what is the average value of the baud rate if c is between 0 and 1.

Line Coding Schemes We can roughly divide the line coding schemes into 5 broad categories.

Unipolar Scheme In a unipolar scheme, all the signal levels are on one side of the time axis, either above or below. NRZ (Non-Return-to-Zero) Traditionally a unipolar scheme was designed as non return to zero scheme in which the positive voltages define bit 1 and the zero voltages define bit 0. It is called NRZ because the signal doesn’t return to zero at the middle of the bit.

Polar Schemes In polar schemes the voltages are on both sides of the time axis. For example the voltage level for 0 can be positive and the voltage level for 1 can be negative. NRZ, In polar NRZ we use two level of voltage amplitude. We can have 2 versions of polar NRZ: NRZ-L and NRZ-I

Return to Zero It describes a line code used in telecommunication signals in which the signal drops (returns to zero) between each pulse. This takes place even a number of consecutive 0’s and 1’s occurs in a signal. The signal is self clocking. This means that a separate clock doesn’t needed to be sent along side the signal, but suffers from twice the bandwidth to achieve the same data rate as compared to NRZ Format.

RZ (Figure)

Introduction Why do we need channel coding and error control for radio communication? You all should be aware of the fact that the medium is not noise less. Also in the case of satellite communication you have limited transmitting power in forward channels (downlink) In wireless communications, message go through the Noise medium between BS and MS and reflection, refraction, diffraction and scattering effects the quality of the signal.

Introduction (Continued)
So any phenomenon that can enhance correct reception of radio signals is always welcome. Channel coding add redundancy information to the original information at the transmitter side. It follows some logical relation with the original information. After reception the receiver receives the encoded data, possibility with the degree of degradation. At the receiver end the original information can be extracted from the relation between the logical and actual information.

Introduction (Continued)
Introduction to this redundancy will cause consumption of more bandwidth. However it offers benefits of recovering from higher bit error rates. In other words the channel coding allows signal transmission power and useful bandwidth as higher degree of redundancy can tolerate a larger number of errors. However yet it is a fact that in wireless communications the traffic consists of compressed data example audio/ video in digital form, that makes them very sensitive to transmission errors.

Definition of Channel Coding
The channel coding can be defined as “the process of coding discrete digital information in a form suitable for transmission, with an emphasis on enhanced reliability” Channel coding is applied to ensure adequacy of transmission quality bit error rate and frame error rate.

Introduction One of the most important control messages sent to MS is its readiness to send information to the BS. In return the BS advises the MS which traffic or information channel is to be used exclusively by that MS for actual information. Such channel allocation is done for the duration of a call from the MS, and such an assignment is done dynamically as needed so that the wireless resources can be used effectively and efficiently.

Introduction (Continued)
In wireless environment, a BS needs a radio connection between a BS and all the MSs in their transmission range. Since wireless communication is categorized by a wide propagation, there is a need to address the issue of simultaneous multiple access by numerous users in the transmission range. User can also receive signals transmitted by other users in the system. In fact many users access the traffic channels when the uplink path from MS to BS is to be established.

Introduction (Continued)
Therefore it is important for users to distinguish among different signals. To accommodate the number of users, many traffic channels needs to be made available. In principle there are three basic ways to have many channels within an allocated bandwidth, they are; 1. Frequency addressed by FDMA 2. Time addressed by TDMA 3. Code addressed by CDMA

Concepts and Models for Multiple Divisions
There are many MSs allocated in the range/ coverage of a BS. A MS must distinguish which signal is meant for itself among many signals being transmitted by other users or BSs. The BS must be able to recognize the signal sent by a particular user. In other words a wireless cellular system, each MS not only can distinguish a signal from a serving BS but also can discriminate signals from the adjacent BS.

Concepts and Models for Multiple Divisions (Continued)
Therefore a multiple access technique is important in mobile cellular system. Multiple Access techniques are based on orthogonalization of signals. A radio signal can be presented as a function of frequency, time or code as; s(f, t, c)= s(f, t) c(t) f is the function of frequency and t is the function of time. when c(t)= 1 s(f, t, c)= s(f, t)

Concepts and Models for Multiple Divisions (Continued)
If a system employs different carrier frequencies to transmit the signal for each user it is called FDMA System. If a system uses distinct time slots to transmit the signal from different users, it is a TDMA system. If a system users different codes to transmit the signal for each user, it is a CDMA system. Let us write to signals Si and Sj both transmitted in the cell space., the orthogonality conditions can be given by using a general mathematical mode, and we formally consider them as;

Explanation In wireless communication, frequency bands are limited and one has to utilize them at the same time. That will allow multiple users to share radio channels simultaneously. To provide simultaneously two way communications duplex communications a forward and reverse channel are necessary. Two types of duplex systems are utilized: FDD and TDD. FDMA mainly use FDD and TDMA use TDD. A number of channels can be used to transfer data in a much higher rate and the technique is called OFDM

FDMA The Orthogonality condition of the two signals in FDMA is given by; There is no overlapping frequency in frequency domain F and the two signals don’t interfere with each other.

FDMA (Continued) FDMA is a multiple access technique that has been widely adopted in Analog system for a portable and wireless mobile telephones. The BS dynamically assigns a different carrier frequency to each active user (MS). A frequency synthesizer is used to adjust and maintain the transmission and reception frequencies.

FDMA (Continued)

FDMA (Continued)

TDMA The orthogonality condition of TDMA is given as;
Because it is based on the division of time, one can easily determine that there is no over lapping in the time axis.

TDMA (Continued) So TDMA splits a single carrier wave into several time slots and distributes slots among multiple users. The communication channels essentially consists of many units i.e. time slots over a time cycle, which makes it possible for one frequency to be efficiently utilized by multiple users. Given that each utilize a different time slot. This system is widely used in the field of Digital Portable and automobile telephone and mobile satellite communications systems.

TDMA (Continued) A TDMA can use two modes FDD and TDD.

TDMA (Continued)

TDMA (Continued)

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