Comparison Of BER Between (15,11) And (7,4) Hamming Codes Using Simulink

Compare the BER of (15,11) hamming codes with those of (7,4) codes using Simulink. Verify your results using the bertool. Also make adequate discussion on the obtained result. 

Digital communication system

Digital communication system is a method of correspondence where the data or the thinking is encoded carefully as circumspect signs and electronically exchanged to the beneficiaries. Digital communication system is a standout amongst the most normally utilized method of communication in the present situation. Associations by and large depend on this mode for all their business communication.

Currently, the digital communication is taking over from the analog systems of communication , a good example of the situation where the digital systems have taken over the analog systems is the telecommunication channel. It is therefore very important and better to have a good know how of the digital communication systems. For the communication to be termed complete, there must pass through a medium. The channel must be there for the communication to be complete, or even for the communication to take place. This is not limited to the kind of channel the communication uses, this might be optical fiber cables, free spaces or even the copper wire.

Assuming that the channel is not shared as required, then transmission of information could only take place in a single one direction creating a lot of shortcomings when it comes to communication.

The time division multiplexing is one of the method that is used for sharing channel, this method involves allowing the user to have full access to the channel though the period that the user has been allowed is very short.

Another method is the frequency division multiplexing, which involves allowing use to have uninterrupted time with the channel for as long time period.

The main objective of this session is to develop a digital communication systems that are effective and efficient enough to completely take over the analog systems of communication. 

This is a system that is used to encode the analog system to a 0s and 1s stream. This PCM encoder uses the codec in changing the analog voltage that is in between  the -2 and the +2 into an 8 bit binary numbers. 

This kind of channel expels all high recurrence components that are inside the information simple analog signal which is more noteworthy than the most astounding recurrence of the message motion, to abstain from associating of the message signal. The figure below shows how low pass filter works.  

The decoder circuit unravels the beat coded waveform to imitate the first flag. This circuit goes about as the demodulator.

To recuperate the first flag from the examined information, a "demodulator" can apply the technique of regulation in switch. After each testing period, the demodulator peruses the following worth and movements the yield flag to the new esteem. Because of these changes, the flag has a lot of high-recurrence vitality caused by associating. To expel these unwanted frequencies and leave the first flag, the demodulator goes the flag through simple channels that smother vitality outside the normal recurrence go  

The contribution to the PCM ENCODER module is a simple message. This should be obliged to a characterized transfer speed and sufficiency extend.

Pulse Code Modulation

The most extreme admissible message transmission capacity will rely on the examining rate that is to be utilized.

The plentifulness extend must be held inside the ± 2.0 volts scope of the TIMS ANALOG REFERENCE LEVEL. This is with regards to the information abundancy limits that is set for every unit simple module.

A well ordered depiction of the task of the module takes after:

1. The module is driven by an outer TTL clock.
2. The info simple message is then inspected occasionally. The example rate is then controlled by the outer clock.
3. The examining is an example and-hold task. This is inward to the module, and it can't be seen by the client . What is held is abundancy of simple message at inspecting moment.
4. Each example adequacy is contrasted and the limited arrangement of abundancy levels. These are inside a range of the ± 2.0 volts (the TIMS ANALOG REFERENCE LEVEL). All this are the framework quantizing levels.
5. Each and every quantizing levels are then allocated  value which is a number, beginning from  value zero for the least (generally negative) stage, with the most astounding number being (L1), and given that L is the accessible number of stages.
6. Each example is allocated a computerized (double) code word speaking to the number related with the quantizing stage that is nearest to the example sufficiency.
7. The code word is then gathered to the time period together with the different bits as this might be required (portrayed underneath). In a TIMS PCM ENCODER (and numerous business frameworks)  solitary additional bit is then included, all huge piece position. This is then once again  1 or  0. All these bits are then utilized by resulting decoders for all outline synchronization.
8. The casings are all transmitted serially. They are all transmitted at an indistinguishable rate from the examples are taken. The serial piece stream shows up at yield of module.
9. Additionally accessible from module is  synchronizing flag .This flags the end of each and every datum outline.

Decoding the PCM is driven by the outer clock also. The signals of the clock are synchronized similarly to that of the transmitter.

The following are the steps for decoding the PCM ;

1. The PCM frame synchronization for the signal is first extracted from the information or taking the information from the transmitter.
2. The binary numbers and values are then extracted , the numbers are the amplitude coded from that which is taken from its sample which is a frame.
3. The quantization stage that the number stands for is then identified
4. The voltage which is proportional to the amplitude stage is generated.
5. The voltage which is the output is presented.
6. The re-construction of the message might be achieved though with some content break down and distortion , this can be done and made possible by the low pass filtering. The module provides a reconstruction which is built in . 

There are extremely just 3 things we must acknowledge  to know keeping in mind the end goal is just to make a sine wave: The recurrence, example rate and the stage. For this crucial case, how about we make a 100Hz sine wave which  utilizes CD quality encoding. .

A sine wave actually keeps on utilizing the Sin() capacity in order to decide the recurrence. From the level of trigonometry, we can easily notice and realize that the time of a sine wave is 360 digress. This simply means that   sine wave finishes a whole transformation in exactly 360 degrees. In form of  radians, that can be assumed as 2 * Pi(the pie). Sin() can shifts from  negative one to positive one. We could likewise realize that the most extreme estimation of  the  16 bit recording is exactly  32,767 and its base esteem is  negative 32,768.   

The amplitude shift keying is a unique type of amplitude modulation that shows all binary information that is in the form of variation in amplitude of flag.

Any signal that is modulated always has their frequency carrier very high. The signal of the binary gives out a zero value for all inputs that are low and gives the output of the carrier for high input when the amplitude shift keying is modulated.

This can also be taken as a type of sufficiency tweak that speaks to advanced information as varieties in the plentifulness of the transporter wave. In the case of  an ASK framework, the double image 1 is spoken to by transmitting a settled adequacy bearer wave and settled recurrence for a bit term of T seconds. On the off chance that the flag esteem is 1 then the bearer flag will be transmitted; something else, a flag estimation of 0 will be transmitted. 

Any computerized regulation plan that is utilizing a limited number of unmistakable signs to speak to the advanced information. Solicit makes use of a limited number from  the amplitudes, each doled out a one of a kind example of twofold digits. Typically, every abundancy encodes an equivalent number of  the bits. Each example of bits frames the image that is spoken to using the specific sufficiency. The demodulator, that is composed of particularly for the image set makes use of  the modulator, then decides the adequacy of the got flag and maps it back to the image it speaks to, consequently recouping the first information. Recurrence and period of the transporter are kept steady. 

Low Pass Filter

The diagram that represents the ASK modulator is made up of the a generator carrier signal. The sequence of the binary which is from the message flag and also band limited filter.   

The transporter generator, sends a nonstop high-recurrence bearer. The paired arrangement from the message flag makes the unipolar contribution to be either High or Low. The high flag shuts the switch, permitting a bearer wave. Henceforth, the yield will be the bearer motion at high information. At the point when there is low info, the switch opens, enabling no voltage to show up. Henceforth, the yield will be low. 

The band-restricting channel, shapes the beat contingent on the abundancy and stage qualities of the band-constraining channel or the beat forming channel. 

In ASK  demodulation, the presence and the absence of the sinusoid only in given interval time is needed to be calculated. The advantage of the ASK is that of simplicity though ASK is too susceptible to noise and interference . the effects of the noise in ASK is that , it affects the amplitude  hence the technique that is used for modulation is then affected by the noise. 

This is to allow the PCM Encoder module output to encode voltages above and below 0V as this is a property of analog message signals such as music and speech.   

As the input voltage increases positively, the number gets bigger.  .

This is because of the small amounts of DC offset.  

Variable DC  = input voltage + DC offsets.

This method attains the desired limit by varying the input range depending on the DC offsets. 

The Binary number gets smaller.  

Typically 5Vp-pv : The value in Table 1 should be about ±2.5V. 

Quantisation Error.  

(2.5V - -2.5V) / 256 = 0.01953125V or 19.53125mV 

Question 15: To reduce quantisation error it’s better to have more quantisation levels between ±2.5V.  

This is because every time it samples the input signal, its voltage is different hence producing different numbers. 

PCM Decoder creates an apparent copy of the message using a finite number of quantisation levels. Thus, it’s not as smooth as the original message. A copy of the sinewave is always included in the original message. 

-Turn the Buffer module’s Gain control clockwise to improve audiblility.

-Usage of Low-pass Filter module’s Gain.

-Frame synchronization using the alternating synchronization bit.  

This is because the reconstructed message is ‘stepped’ and can only get closer to the original but not become identical. Higher frequencies yield better results.  

The Digital Signal and presence of carrier in the ASK signal are set up to demonstrate how interruption and Distortion of data due to interference.   

ASK  is as a result of multplexing digital data using AM signal.  

This is because some of the recovered message’s higher frequency harmonics are removed by the product detector’s low-pass filter, leading to the distortion in the signal. 

A Comparator.   

A comparator normally changes its output state when the voltage between its inputs crosses through approximately zero volts 

Experiment 11: ASK Demodulation Using Product Detection. 

Conclusion

Conversion from analog systems of communication to digital systems of communication has really helped to improve communication means in the world. It is therefore great and very important to understand how communication is being converted to digital.

Through the introduction of digital communication, we are now able to share anything around the world since communication devices are now going mobile hence portable.

It is therefore recommended that digital communication system be changed to digital so that the ways of exchanging ideas among people might improve more and more.  

References

1. Xiong, F., 2005. Amplitude shift keying. Encyclopedia of RF and Microwave Engineering.
2. Xiong, F., 2003. M-ary amplitude shift keying OFDM system. IEEE Transactions on Communications, 51(10), pp.1638-1642.
3. Weber, W.I.I.I., 1978. Differential encoding for multiple amplitude and phase shift keying systems. IEEE Transactions on Communications, 26(3), pp.385-391.
4. Jung, D.Y., Chang, W.I., Eun, K.C. and Park, C.S., 2007. 60-GHz system-on-package transmitter integrating sub-harmonic frequency amplitude shift-keying modulator. IEEE transactions on microwave theory and techniques, 55(8), pp.1786-1793.
5. Black, H.S. and Edson, J.O., 1947. Pulse code modulation. Transactions of the American Institute of Electrical Engineers, 66(1), pp.895-899.
6. Proakis, J.G., 2001. Companders. John Wiley & Sons, Inc..
7. Mayo, J.S., 1968. Pulse-code modulation. Scientific American, 218(3), pp.102-109.
8. Cattermole, K.W., 1969. Principles of pulse code modulation.
9. O'neal, J.B., 1966. Predictive quantizing systems (differential pulse code modulation) for the transmission of television signals. Bell Labs Technical Journal, 45(5), pp.689-721.
10. Goodall, W.M., 1951. Television by pulse code modulation. Bell Labs Technical Journal, 30(1), pp.33-49.
11. O’Reilly, J.J., 1984. Pulse code modulation. In Telecommunication principles(pp. 86-96). Springer, Dordrecht.
12. Peebles Jr, P.Z., 1987. Digital communication systems. Englewood Cliffs, NJ, Prentice-Hall, Inc., 1987, 445 p.
13. Lathi, B.P., 1998. Modern Digital and Analog Communication Systems 3e Osece. Oxford university press.
14. Sklar, B., 1997. Rayleigh fading channels in mobile digital communication systems. I. Characterization. IEEE Communications magazine, 35(9), pp.136-146.
15. Wicker, S.B., 1995. Error control systems for digital communication and storage(Vol. 1). Englewood Cliffs: Prentice hall.
16. Jeruchim, M., 1984. Techniques for estimating the bit error rate in the simulation of digital communication systems. IEEE Journal on selected areas in communications, 2(1), pp.153-170.
17. Lucky, R.W., 1966. Techniques for adaptive equalization of digital communication systems. Bell Labs Technical Journal, 45(2), pp.255-286.
18. Roden, M.S., 1991. Analog and digital communication systems. Englewood Cliffs, NJ, Prentice Hall, 1991, 521 p.
19. Shanmugam, K. and Balaban, P., 1980. A modified Monte-Carlo simulation technique for the evaluation of error rate in digital communication systems. IEEE Transactions on Communications, 28(11), pp.1916-1924.
20. Lathi, B.P., 1995. Modern digital and analog communication systems. Oxford University Press, Inc..
21. XIN, J.T., ZHANG, Q., ZHEN, Y.F. and XIE, S.M., 2008. CPC Hydraulic System Modeling and Simulation. Equipment Manufacturing Technology, 1, p.005.
22. Yingjie, L.X.Y., 2009. Building and Application of Mineral Processing Block Library Based on SIMULINK [J]. Metal Mine, 6, p.048.
23. Grant, M., Boyd, S. and Ye, Y., 2008. CVX: Matlab software for disciplined convex programming.
24. Brown, R.G. and Hwang, P.Y., 1997. Introduction to random signals and applied Kalman filtering: with MATLAB exercises and solutions. Introduction to random signals and applied Kalman filtering: with MATLAB exercises and solutions, by Brown, Robert Grover.; Hwang, Patrick YC New York: Wiley, c1997.