INSTITUTE OF AERONAUTICAL ENGINEERING

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1 INSTITUTE OF AERONAUTICAL ENGINEERING (AUTONOMUS) Dundigal, Hyderabad ELECTRONICS AND COMMUNICATION ENGINEERING TUTORIAL QUESTION BANK Name : DIGITAL COMMUNICATIONS Code : AEC009 Class : B. Tech V Semester Branch : ECE Academic Year : 0 09 Coordinator : Dr. Prasantha Kumar, Professor, ECE Faculty : Mr. J. Siva Ramakrishna, Assistant Professor, ECE Mrs. G. Mary Swarna Latha, Assistant Professor, ECE COURSE OBJECTIVES: The course should enable the students to: S. NO DESCRIPTION I the different digital modulation techniques. II Discuss the importance of error detection and correction codes and use them in presence of channel noise. III Describe and analyze the methods of transmission of digital data using baseband and carrier modulation techniques. IV Decompose codes separately into source codes and channel codes and develop competency in modeling and analyzing communication system elements. COURSE LEARNING OUTCOMES: Students, who complete the course, will have demonstrated the ability to do the following: CAEC009.0 CAEC00.0 CAEC009.0 CAEC009.0 CAEC009.0 CAEC CAEC009.0 CAEC009. the basic concepts of pulse amplitude modulation (PAM), pulse position modulation (PPM) and pulse width modulation (PWM). Describe the advantages and disadvantages of digital communication systems and remember the concept of pulse code modulation technique. the concept of sampling, quantization and coding. and remember the concept of amplitude shift keying modulation and demodulation. Analyze the frequency shift keying modulator, coherent and noncoherent frequency shift keying detectors. Describe the difference between binary phase shift keying ad quadrature phase shift keying techniques. the concept of baseband transmission and various line coding formats used in digital communication systems. Describe the significance of pulse shaping to reduce inter-symbol interference in digital communications. the operation of raised cosine filter and eye patterns of various ASK, PSK and FSK digital modulation techniques.. and the concept of mutual information and entropy in information theory. Design various mathematical modeling schemes for communication channel and determine their channel capacity. Analyze various spread spectrum modulation schemes such as direct sequence spread spectrum and frequency hopping spread spectrum.

2 CAEC009. CAEC00. CAEC00. Analyze the significance of linear block codes and convolution codes in digital communications. Interpret the difference between hamming codes and binary cyclic codes. various types approaches such as time domain approach and transform domain approach for implementation of convolution codes. Design different types of error detection and correction techniques for linear block codes and convolution codes. Acquire experience in building and troubleshooting simple digital communication system using digital modulation and demodulation techniques. Acquire the knowledge and develop capability to succeed national and international level competitive examinations.

3 TUTORIAL QUESTION BANK UNIT-I PULSE DIGITAL MODULATION PART-A (SHORT ANSWER QUESTIONS) Discuss about the simplified Block diagram of an Electronic communication system Describe the Pulse Modulation and types of pulse modulation techniques. Discuss the advantages and disadvantages of digital communication system Define Nyquist rate and sampling theorem. Discuss about quantization and their types. Discuss about uniform quantization? Mention two major sources of noise which influence the performance of a PCM system. List out the advantages of ADM over DM. 9 List out the advantages of DPCM over PCM. 0 Discuss the advantages of DM over PCM Compare the features of PCM and DPCM Discuss about Quantization error. Discuss about companding in PCM. CAEC009.0 List the applications of Digital communication systems. Discuss the advantages and disadvantages of PCM Discuss the advantages and disadvantages of PAM Discuss the advantages and disadvantages of PWM Discuss the advantages and disadvantages of PPM 9 List the applications of Pulse Code Modulation. 0 List the applications of Pulse Amplitude Modulation. List the applications of Pulse Width Modulation. List the applications of Pulse Position Modulation. PART-B (LONG ANSWER QUESTIONS) 9 Describe the Model of Digital Communication Systems with neat diagrams and list the advantages of digital communications over analog communications. Discuss about Pulse Amplitude Modulation(PAM),Pulse Width Modulation (PWM) and Pulse Position Modulation(PPM) techniques with neat diagrams. Discuss quantization error? How does it depend upon the step size? Suggest some methods to overcome the difficulties encountered depending on the modulating Amplitude swing? Describe the process of Sampling and Quantization in digital Communication. What is aliasing effect in sampled signal? How aliasing can be eliminated? Explain with neat diagram. Explain a)channel Noise b) Quantization noise in Delata Modulation(DM) and derive expression for them? Explain the generation of pulse code modulation(pcm) with a neat diagramand also discuss quantization noise and signal to noise ratio in PCM. Describe Delta Modulation(DM) system. Also discuss the slope overload distortion and granular noise present in it. (a) Discuss the working of a quantizer and the need of the quantizer used in digital pulse modulaton techniques. (b) Explain in detail about non-uniform quantization. Discuss about Pulse code modulation and different types of noise effects in pulse code modulation.

4 0 (a) Explain the basic principle of DPCM and working of DPCM transmitter and receiver with the help of diagram. (b) Derive an expression for channel noise in delta modulation. What is aliasing effect in sampled signal? How aliasing effect can be eliminated? Explain with neat diagram. Discuss the drawbacks of Delta modulation and how they overcome using adaptive delta modulation. PART-C (PROBLEM SOLVING AND CRITICAL THINKING QUESTIONS) Specify the Nyquist rate and the Nyquist interval for each of the following signals: a)g(t)= sinc(00t) b) g(t)= sinc (00t) c) g(t)= sinc(00t)+ sinc (00t) 9 A signal m(t)= Cos (0 πt) + Cos (0πt) +Cos (0 πt) is sampled at0 Hz, Hz,00 Hz.Estimate the frequency components of the signal that appear at the output of an ideal LPF with cutoff at 90 Hz. in each case. What is the Nyquist rate of sampling and Nyquist interval form (t)? Determine the processing gain of a DPCM system with a first order predictor, if the message signal has a normalized auto-correlation function of 0. for a lag of one period, assuming that the predictor is designed to minimize the mean square value of the prediction error. Find the signal amplitude for the maximum slope overload error in a DM system. If the step size is V with a repetition period of msec. the information signal frequency of 00 Hz. Find the maximum amplitude of a KHz sinusoidal signal input to a delta modulator that will prevent slope overload, when the sampling rate is 0,000 samples/sec and the step size is = 0.. Let m(t) = Am cos(πfmt) be the input to a delta modulator with parameters (step size) and Ts (sampling period). Show that the minimum sampling frequency fs,min, needed to avoid slope overload distorsion, is given by fs,min = π fm Am/. The input to the PCM system is m(t)=0cosπx0t, the signal is sampled at nyquist rate, each sample is encoded in to -bits. Determine i) Bit rate ii) Bandwidth, iii) Signal to Noise ratio For a DM system, signal sampled at KHz and Amax = (a) Assuming that the signal is sinusoidal determine output signal power & SNR. (b) Determine the minimum transmission Band width? Derive the relations A voice frequency signal band limited to KHz is transmitted with the use of the DM system. The prf is 0,000 pulses/second and step size is 0 mv. Determine the maximum permissible speech signal amplitude to avoid error. CAEC009.0 CAEC009.0 CAEC In a binary PCM system,the output to signal to quantization noise signal is to be held to be a minimum of 0db.Determine the number of required levels and find the corresponding output signal to quantization ratio. UNIT-II DIGITAL MODULATION TECHNIQUES PART-A(SHORT ANSWER QUESTIONS) Construct the ASK waveforms for 00. CAEC009.0 Sketch the block diagram of ASK generation. CAEC009.0 Construct the FSK waveforms for 00. CAEC009.0 Show the space representation of BPSK Explain the Bandwidth, power and energy calculations for PSK signal. Explain why PSK is always preferable over ASK in coherent detection? CAEC009.0 Distinguish between Coherent and Non coherent detection? CAEC009.0 Explain Phase shift keying with relevant equations and waveforms. 9 Estimate the band width required for frequency shift keying CAEC009.0

5 0 Explain non coherent detection of Amplitude shift keying. CAEC009.0 Construct the constellation diagram for Quadrature phase shift keying. Explain coherent detection of frequency shift keying. CAEC009.0 Construct the FSK waveforms for a given input data 0. CAEC009.0 Define the probability of error CAEC009.0 Draw FSK spectrum CAEC009.0 What should be the relationship between bit rate and frequency shift for a CAEC009.0 better performance? Show the space representation of QPSK What is the probability of error for ASK, FSK, BPSK. CAEC What is the probability of error using matched filter. 0 What is a optimum and matched filter? CAEC009.0 Explain the advantages of Coherent modulation schemes. CAEC009.0 PART-B (LONG ANSWER QUESTIONS) Explain in detail about modulation and demodulation of i)frequency Shift Keying(FSK) ii)phase Shift Keying(PSK) with waveforms and equations. Explain Differential Phase Shift Keying modulation(dpsk) and demodulation with neat block diagrams and also sketch the binary PSK for the bit sequence a)draw the block diagram of QPSK demodulator and explain in detail. (b) Derive a relation for probability of error and band width in Quadtrature Phase Shift Keying. Draw the structure of the receiver for an orthogonal wideband FSK signaling scheme and derive a relation for probability of error. (a) Compare digital modulation systems Amplitude shift keying(ask),frequency shift keying(fsk) and Phase shift keying(psk). (b) Explain the theory of matched filter receiver. (a) Derive an expression for probability of error in Frequency shift keying system. (b) Show that BPSK is superior to ASK by db in the average signal power requirement with appropriate mathematical derivations. (a) Derive an expression for probability of bit error of a binary coherent FSK receiver. (b) Derive an expression for probability of bit error of a binary noncoherent ASK. Discuss about Quadrature Phase Shift Keying in detail with an example and draw the waveforms and sketch the QPSK waveform for the sequence Explain Differential phase shift keying modulation and demodulation with 9 neat block diagram. Draw the wave forms for the bit stream 0000 using DPSK. Draw the block diagram of Amplitude shift keying modulator and 0 demodulator and explain in detail and sketch the ASK waveform for the sequence With neat diagrams explain the generation of Differntially encoded phase shift keying and sketch the Frequency shift keying waveform for the sequence PART-C (PROBLEM SOLVING AND CRITICAL THINKING QUESTIONS) In a binary PSK scheme using correlation receiver, the local carrier waveform is A cos(w c t+ѳ) instead of A cos(w c t) due to poor carrier synchronization. Derive an expression for the probability of error and compute the increase in error probability when ѳ= anda T b /Ƞ =0. The bit stream 0000 is to be transmitted using DPSK. Determine the encoded sequence and the transmitted phase sequence. CAEC009.0 CAEC009.0 CAEC009.0 CAEC009.0 CAEC009.0

6 CAEC009.0 For the signals, the given bit rate is 0Kbps. Estimate the bandwidth for AmplitudeShist Keying and Frequency Shift Keying signals. Assume that 00 bits/sec data is sent over a pass band channel by Frequency Shift Keying signaling scheme. Estimate the transmission bandwidth. CAEC009.0 A voice signal is sampled at the rate of 000samples/sec and each sample is encoded into -bits using PCM system. The binary data is transmitted into free space after modulation. Determine the bandwidth of the modulated signal, if the modulation used is a) ASK b) PSK c) FSK where f=mhz and f=mhz Binary data is transmitted over an RF band pass channel with a usable CAEC009.0 bandwidth of 0MHz at a rate of.x0bits/sec using an ASK signaling method. The carrier amplitude at the receiver antenna is mv and noise power spectral density at the receiver input is 0-Watt/Hz. Determine the error probability of a coherent receiver. Assume that 00 bits/sec random data are sent over band pass channel by CAEC009.0 using the following schemes: A) BPSK b) FSK Determine the Transmission bandwidth Binary PSK (BPSK) is used for data transmission over an AWGN channel with power spectral density N0/ = 0 0 W/Hz. The transmitted signal energy is Eb = A T /, where T is the bit duration and A is the signal amplitude. Determine the value of A needed to achieve an error probability of 0, if the data rate is: (a) 0 Kbit/s (b) 00 Kbit/s (c) Mbit/s Find z = Eb/N0 required to give Pb = 0 for the following coherent digital 9 modulation schemes: (a) on-off keying (ASK), (b) BPSK, (c) BFSK and (d) BPSK with a phase error of deg. The bit stream 0000 is to be transmitted using Differential Phase 0 Shift Keying. Determine the encoded sequence and the transmitted phase sequence UNIT-III BASE BAND TRANSMISSION AND PULSE SHAPING PART-A(SHORT ANSWER QUESTIONS) What are the requirements of line encoding format. CAEC009.0 List the various types of line encoding formats. CAEC009.0 What is Unipolar line encoding format. CAEC009.0 What is Polar line encoding format. CAEC009.0 What is Bipolar line encoding format. CAEC009.0 Write the advantages and disadvantages of Unipolar line encoding format. CAEC009.0 Write the advantages and disadvantages of Polar line encoding format. CAEC009.0 Write the advantages and disadvantages of Bipolar line encoding format. CAEC What is BZS Scrambling technique? CAEC What is HDB Scrambling technique? CAEC009.0 Draw the NRZ and RZ code for the digital data 0000 CAEC009.0 Draw the RZ- bipolar line code for the information {00} CAEC009.0 CIE II List out the use of eye patterns CAEC State any applications of eye pattern CAEC State Nyquist criterion for zero ISI. CAEC009.0 How does pulse shaping reduce inter symbol interference? CAEC009.0 How do we get eye pattern? What you infer from this? CAEC ISI can-not be avoided. Justify the statement. CAEC What is correlative coding? CAEC009.0 What is Inter symbol interference? CAEC What is Raised cosine filter? CAEC What is equalization? CAEC009.0 PART-B (LONG ANSWER QUESTIONS) Explain in detail about Unipolar line encoding format and represent the data 0000 using the unipolar RZ and unipolar NRZ digital data format. CAEC009.0

7 Describe about detail about Polar line encoding format and represent the data 0000 using the polar RZ and polar NRZ digital data format. CAEC009.0 Discuss in detail about Bipolar line encoding format and represent the data 0000 using the bipolar NRZ digital data format. CAEC009.0 Explain in detail about BZS Scrambling technique represent the data using using the BZS Scrambling technique. CAEC009.0 Discuss in detail about HDB Scrambling technique represent the data using using the HDB Scrambling technique. CAEC009.0 Draw Power Spectral Density for various line encoding formats and CAEC009.0 represent the Bipolar NRZ,split phase Manchester,polar RZ and AMI for the bit strem CIE II Describe how the inter symbol interference(isi) in data transmission can be studied with the help of a display in the oscilloscope called eye diagram. CAEC What is meant by Cross talk? Explain in detail about the causes for cross CAEC talk in base band transmission. What is the need of pulse shaping for optimum transmission in baseband CAEC009.0 transmission? Explain. Discuss the information about performance of a system provided by the eye CAEC pattern. Draw the eye diagram for Amplitude Shift Keying, frequency shift keying and phase shift keying. Define eye diagram. Draw the eye diagram for PSK. CAEC Draw and explain the block diagram of modified duo-binary signaling CAEC009.0 scheme Consider the binary sequence b k = 0000 applied to the input of a precoded modified duobinary sequence.determine the sequence a k at the precoder output. Explain how Inter Symbol Interference(ISI) occurs in base-band binary data CAEC009.0 transmission system and describe the pulse shaping method to minimize ISI. Describe the Nyquist bandwidth requirement of raised cosine filter for CAEC009.0 distortion less transmission and define roll off factor. Draw and explain the block diagram of duo-binary signaling scheme for CAEC controlled ISI.Show that the binary sequence 0000 can be detected in the absence of noise irrespective of the choice of the extra bit. PART-C (PROBLEM SO LVING AND CRITICAL THINKING QUESTIONS) A line coding scheme uses Unipolar NRZ and RZ encoding with CAEC009.0 rectangular pulses. Sketch the signal corresponding to the bit sequence 00. A line coding scheme uses Polar NRZ and RZ encoding with rectangular CAEC009.0 pulses. Sketch the signal corresponding to the bit sequence 000. A line coding scheme uses Bipolar NRZ and RZ encoding with rectangular CAEC009.0 pulses. Sketch the signal corresponding to the bit sequence 00. A scrambling coding scheme uses BZS with rectangular pulses. Sketch the signal corresponding to the bit sequence CAEC009.0 A scrambling coding scheme uses HDB with rectangular pulses. Sketch the signal corresponding to the bit sequence CAEC009.0 CIE II The Fourier transform P(f) of the basis pulse p(t) employed in a certain binary communication system is given by CAEC009.0 P(f) = {0 ( ( f / 0 )) if 0 f(hz) 0 ; =0 other wise. (a) From the shape of P(f), explain whether this pulse satisfies the Nyquist criterion for ISI free transmission. (b) Determine p(t) and verify your result in part a. (c) If the pulse does satisfy the Nyquist criterion. What is the transmission rate (in bits/sec.) and what is the roll-off factor? In a certain telemetry system, eight message signals having khz bandwidth each are time division multiplexed using a binary PCM Technique.the error in sampling amplitude cannot be greater than % of the peak amplitude. Determine the minimum transmission bandwidth required if raised cosine pulses with roll off factor α=0. are used the sampling rate must be at least % above the Nyquist rate. A certain telephone line bandwidth is KHz. Calculate the data rate in bps that can be transmitted if we use binary signaling with raised cosine pulses and a roll off factor α=0.. CAEC009.0 CAEC009.0

8 CAEC009.0 A telephone line of bandwidth Khz required to transmit data at kbps using raised cosine pulses. Determine the roll of factor α The unequalized pulse in a PAM system has the following values at CAEC009.0 sampling times: pr(ktb) =pr(k)=0. for k=; =0. for k=0; =0. for k=-; =0 for IkI>; a)design a three-tap zero forcing equalizer so that the equalizer output is at k = 0 and 0 at k=± b)calculate P eq (k) for k=±,±. UNIT-IV INFORMATION THEORY AND SOURCE CODING PART-A(SHORT ANSWER QUESTIONS) Define conditional entropy. CAEC009.0 List out the applications of CDMA. CAEC009.0 Define spread spectrum. List its uses. CAEC009. What is Hartley Shannon law? CAEC009. Define Entropy. CAEC009.0 Derive the Expression for the Information Rate. Briefly explain about Spread spectrum. CAEC009. What is Frequency hopping spread spectrum? CAEC State four applications of spread spectrum. CAEC Discuss the applications of spread spectrum modulation? CAEC009. Show that information contained by a symbol is inversely proportional to the probability of that symbol. Show that the entropy is maximum when all the symbols are equi probable. CAEC009.0 Assume M=. Discuss Various mathematical modeling of communication channels and their capacities. Write any two differences between Fixed length and variable length Source CAEC009.0 Coding Schemes. Discuss how Source coding is used to increase average information per bit. CAEC009.0 PART-B (LONG ANSWER QUESTIONS) A source emits ondependent sequences of symbols from a source alphabet CAEC009.0 containing five symbols with probabilities 0., 0., 0., 0. and 0. compute the entropy of the source.. Show that H(X, Y) = H(X) + H(YIX) = H(Y) + H(XI Y). Show that (a) H(XI Y) = H(X) when X and Yare statistically independent, and (b) H(Xi Y) = 0 when X = Y. What are the characteristics of PN sequences? Explain For a source emitting symbols in independent sequences, show that the source entropy is maximum when the symbols occur with equal probabilitiesdescribe the process of code division multiple access in detail. A binary source is emitting an independent sequence of O's and 's with CAEC009. probabilities p and - p, respectively. Plot the entropy of this source versus p (0 < P < ). Describe with a neat sketch the direct sequence Spread spectrum technique. Define spread spectrum system, applications of spread spectrum and what are the various types of the system. How spread spectrum methods are classified and what is the basis of classification. What are pseudo-noise sequences and why they are used in spread spectrum modulation.. CAEC009. CAEC009.0

9 CAEC Describe the role of code division multiple access technique in present generation? 0 Give a brief history about direct sequence spread spectrum. CAEC009. A source emits four symbols with probabilities P 0, P, P, and P. Find out CAEC009. the amount of information obtained due to these four symbols.. What is meant by Synchronization? Why we require synchronization in CAEC009. spread spectrum? Explain in detail. A source transmits two independent messages with probabilities of P and (- P) respectivily. Prove that the entropy is maximum when both the messages are equally likely. Show thayt if there are M number of equally likely messages, then entropy of the source is log M. Prove that the capacity of a white band limited Gaussian channel is B log (+ ) bits/sec. Define the following, CAEC009.0 i)information ii) Entropy iii) Rate of Information iv) Channel Capacity 9 Show that the source entropy is maximum when symbols occur with equal probabilities. A code is decomposed of dots and dashes. Assume that the dash is times as long as dots and it has one third the probability of occurance. Calculate average information in dot-dash code and information in a dot, a dash. For a symmetric or uniform channel, there are M number of output messages and N number of input messages determine the capacity of the channel. Prove that mutual information of the channel is symmetric i.e, I(X;Y) = 0 I(Y;X). PART-C (PROBLEM SOLVING AND CRITICAL THINKING QUESTIONS) A source is transmitting Four symbols A, B, C and D with probabilities /, /, / and / respectively. Find the entropy of the source and find information rate if r= messages/sec. In a message conveyed through a long sequence of dots and dashes, the probability of occurrence of a dash is two third of that of dot. The duration of a dash is four times that of a dot. If a dot losts for 0msec and the same time is allowed between symbols, determine i)the information in dot and dash ii)average information in dot-dash code iii)average information rate A source is transmitting the symbols A and B with probabilities / and / respectively. Calculate the Entropy of the source and the required channel capacity using the simplest code and also coding efficiency. One of five possible message Q to Q having probabilities /, /, /, /, / respectively are transmitted. Generate Huffman code and Calculate the coding efficiency If I(x) id the information carried by symbol x and I(x) id the information carried by symbol x then prove that the amount of information carried compositely due to xand x is I(x, x)= I(x) I(x) Consider a telegraph source having two symbols, dot and dash. The dot duration is 0.. The dash duration is times the dot duration. The probability of the dot s occurring is twice that of the dash and the time between symbols is 0. sec. Calculate the information rate of the telegraph source. A discrete memory less source has an alphabet of seven symbols with probability for its output, as described here: Symbol prob. S₀ 0., S₁ 0.,S₂ 0.,S₃ 0., S₄ 0., S₅ 0.0 and S₆ 0.0 (i) Compute the CAEC009.0 CAEC009.0 CAEC009.0 CAEC009.0

10 Huffman code for this source and explain why the compute source code has an efficiency of 00 percent. (ii) Calculate H. Apply Shannon fano coding for the messages with probabilities 0., 0., CAEC , 0., 0. and find the coding efficiency 9 Consider a discrete memory less source with source alphabet S={s0, s, s} and source statistics {0.,0.,0.}.Calculate the entropy of source. 0 An event has six possible outcomes with the probabilities P= ½, P= ¼, CAEC009.0 P= /, P=/, P= /, p=/. What is the entropy of the system? A DMS X has symbols x, x, x, x with p(x) =/, p(x) =/, p(x) =/= p(x).construct Shannon-fanocode.Repeat for the Huffman code and compare the results UNIT-V LINEAR BLOCK CODES AND CONVOLUTIONAL CODES PART-A(SHORT ANSWER QUESTIONS) Mention the properties of cyclic code. Write the advantages of convolution codes. Explain in one sentence about (i) Block Size (ii) Linear block codes. List out Properties of Cyclic Codes. List the advantages and disadvantages of convolutional codes. What are cyclic codes? List the advantages and disadvantages of it. Discuss the difference between convolutional code and block code. Explain how syndrome is calculated in Hamming codes and cyclic codes? 9 Define code word & block length. 0 What is the code length of a convolution code? What are the conditions to satisfy the hamming code? Explain about the Convolutional interleaving. PART-B (LONG ANSWER QUESTIONS) 9 0 For a linear block code, prove that the syndrome depends only on error pattern and not on transmitted codeword. For a linear block code, prove that all the error patterns that differ by a codeword have the same syndrome.. Consider an (n,k) linear block code with generator matrix G and parity check matrix H. the (n, n-k) code generated by H is called the dual code of (n, k) code. For a linear block code which corrects single error per code vector, prove that n k = log (n+) and hence design a linear block code with a minimum distance of three. Show that the syndrome S corresponds to rows of H T representing error location in error pattern. Explain about Error detection and Correction capabilities of Hamming codes. Explain how Parity checking can be used for error detection or error correction. For a linear block code, prove with example that: i) The Syndrome depends only on error pattern and not on transmitted code word? ii) All error patterns that differ by a codeword have the same syndrome? What is the structural representation of Linear Block codes and give the Matrix description of Linear Block codes. Explain about block codes in which each block of k message bits is encoded into block of n > k bits with an example. Write short notes on following with examples: a) Convolutional codes b) Viterbi Decoding. With an example explain the error correction capability using Hamming codes

11 a) What is the significance of Trellis structure? Explain b) With neat sketch explain the procedure for Syndrome calculation. What is the use of syndrome? Draw the (n-k) syndrome calculation circuit for (n,k) cyclic code? Explain A generator polynomial of a (, ) cyclic code is G(p) = p + p +. Find the code vectors for the code in nonsystematic form. Find the possible generator polynomials (, ) cyclic code. Find out the code vector corresponding to these generator polynomials. Design syndrome calculator for a (, ) cyclic hamming code generator by the polynomial G(p) = p + p +. Consider the (, 9) cyclic code generated by G(p) = p + p + p + p +. This code has a burst error correcting ability of q =. Find burst error correcting efficiency of this code. 9 Construct a systematic (, ) cyclic code using the generator polynomial g(x) = x + x+. What are the error correcting capabilities of this code. PART-C (PROBLEM SOLVING AND CRITICAL THINKING QUESTIONS) Decode the given sequence of a convolutional code with a code rate of r=/ and constraint length K=, using viterbi decoding algorithm. Consider (, ) linear code whose generator matrix is- G= : : : : 0 (i) Find all code vectors of this code. (ii)find the parity check matrix for this code. (iii) Find the minimum weight of this code. (iv) Prove equation CHT=0 Draw the code tree of a Convolutional code of code rate r=/ and Constraint length of K= starting from the state table and state diagram for an encoder which is commonly used. Draw the trellis diagram of a Convolutional code of code rate r=/ and Constraint length of K= starting from the state table and state diagram for an encoder which is commonly used. For a (, ) systematic linear block code, the three parity check bits c, c, c are formed from the following equations. C=d+d C=d+d+d C=d+d a) Construct the generator matrix G. b) Construct all possible code words Consider the (,) linear block code with G= (a) Construct all the possible code words (b) Construct all the single error patterns For a cyclic code the generator polynomial g(x) = (x+x+). a) If the received code is 0000, determine the transmitted data. b) If the received code is 00, determine the transmitted data. Consider a (,) cyclic code with generator polynomial g(x)= (x+x+).determine the code for data bits 00,, and 000 Consider the (,,) nonsystematic convolution encoder with g (0) = (,, 0), g () =(,0,),g ()=(0,,). Find the constraint length and the rate efficiency of the code.

12 9 0 Consider the (,,) nonsystematic convolution encoder with g (0) = (,, 0), g () =(,0,),g ()=(,,). What the generator matrix for this code Find the code word for data word 0 in a (,) cyclic code using the generator polynomial g(x)=+x+x using encoder Construct all the possible systematic code words for (,) cyclic code with the following generator polynomial g(x)=x0+x +x +x +x +x+. Construct the encoder circuit for this. For a (,) systematic linear block code the three parity check bits c, c, c are formed from the following equations: c=d (xor) d ; c= d (xor) d (xor) d; c= d (xor) d. a) Write down the generator matrix G b) Suppose that the received word is 00. Decode this received word by finding the location of the error and the transmitted data bit HOD, ECE