Session. Semester - 2 - 2016/2017. Assessment title/description. Concepts and applications of communications. Module name and Number Communication systems and computer networks (16-5117). Hand out week. Uploaded week 28 onto Blackboard. Hand in method and date. Upload a PDF of your assignment and the Excel file yourname.xls and MATLAB file your_name3aii onto Blackboard by 23.59 on the 20th March 2017. Late submission penalty. No marks will be awarded for a late submission. Answer all questions showing all relevant working. All questions carry equal marks. It is important that you show your attempt at reaching a solution and detail your methodology, as this may attract marks, even if the correct solution is not arrived at. Some parts of the questions will require you to research around the topic. Solutions based on individual work, should be submitted. The University Regulations on academic conduct, including cheating and plagiarism, apply to this assignment. 1). a). i). Determine the self-information and the entropy of the following four symbol probability distribution that originates from a discrete memory less source. p(A) = 0.1, p(B) = 0.2, p(C) = 0.305, p(D) = 0.395. Suggest a set of codes for this distribution and determine the coding efficiency for your codes. ii). A data source generates 100 (equiprobable) discrete memory-less symbols. It is to be source encoded using a size ten alphabet. The 100 code words in figure 1. are suggested to identify each symbol. Comment on this choice of coding alphabet and code words including calculations based on related information theory concepts. . A BA CA DA EA FA GA HA IA JA B BB CB DB EB FB GB HB IB JB C BC CC DC EC FC GC HC IC JC D BD CD DD ED FD GD HD ID JD E BE CE DE EE FE GE HE IE JE F BF CF DF EF FF GF HF IF JF G BG CG DG EG FG GG HG IG JG H BH CH DH EH FH GH HH IH JH I BI CI DI EI FI GI HI II JI J BJ CJ DJ EJ FJ GJ HJ IJ JJ Figure 1. iii). An alphabet gave the following probability distribution 0.5, 0.4 and 0.1. Encode the alphabet into binary words using the Huffman coding method and determine the coding efficiency. Compare with fixed length encoding. Explain how the efficiency could be increased even further using a method that is still based on Huffman coding. Discuss the effect on relevant communication system parameters when using these codes. [25 marks] 2). a). A binary symmetric channel is shown in figure 3.1.x0, p(x0) y0 y1 1 - p 1 - p p p x1, p(x1) Figure 3.1 binary symmetric channel. Explain the meaning of each of the variables the following expression and describe how you would use this to determine a value for Z that relates to figure 3.1. You don't need to know what is the purpose of Z. ∑∑ − = − = Z = M m 0 1N n 0 1 p(xm) p(yn | xm)log⎜ ⎜ ⎝ ⎛ p(yn1| xm) ⎟ ⎟ ⎠ ⎞ Then given for a binary source p(x0) = 0.3, p = 0.15 calculate Z. b). Plot a suitable graph that depicts the entropy (as the dependent variable) of a binary symmetric channel and considers all relevant parameters. [25 marks] 3). a). i). An analogue signal with a range of 0 to 5 V is to be pulse code modulated and is to have a dynamic range of at least 45 dB. Calculate: the number of bits used for quantisation the step size the increase in dynamic range, as a dB, if the number of bits used for quantisation is subsequently doubled. ii). have a look at the quantiz function in MATLAB and use this to quantise the signal y(t) = sin(2πft) + sin(2πft + π/4) to eight levels using a sample frequency of 10×f, where f = 100 (MATLAB gives example code as to how to use this function). Describe the noise produced from the quantisation process as fully as you can. Use linear quantisation. Save and submit the MATLAB f1le as your_name3aii. iii). A message signal has a frequency content that can range from 0 to 0.25 kHz (assume all frequencies within this range have the same amplitude) and is sampled by a pulse train consisting of regularly spaced pulses separated by 1 ms with a width of 0.5 ms. The amplitude of the message signal is between 1 and 0. Using appropriate signal sketches and any relevant associated plots discuss the effect of this in relation to the parameters given. [25 marks] 4). a). A two level amplitude shift keying scheme (ASK) is implemented using square pulses of 1 microsecond duration (non return to zero) and amplitudes 1V and 5 V. The carrier frequency is a sinewave of 5MHz with amplitude 1 V. i). Sketch the two possible modulated waveforms and state the data rate assuming the pulses represent a 0 and a 1 respectively. Compare this with a method that uses four levels. b).A modulated signal is given as Vc(t) =10sin(2π106t +θ(t)) where θ(t) = 3×π×m(t) and m(t) is the modulating signal (message). Plot a labelled graph in Excel of 2π106t +θ(t) and Vc(t) =10sin(2π106t +θ(t)) for m(t) = 0 to 1 (time scale over this range is t = 0 to 1e-6). Explain how this can be used to implement digital modulation. Include the plots in your assignment. Section b). of this question is to be saved in an Excel file in a worksheet labelled Q2b with the Excel file name yourname.xls that displays relevant plots, and is to uploaded onto Blackboard by the date and time given in the assignment.c).Consider the following expression. ⎞⎟⎠ ⎛⎜⎝ ( ) = ( )×cos + 2 (k −1) K y t p t t π ω where p(t) is a rectangular baseband pulse shape and k = 1,2,3,…. K. i. Explain what type of modulation scheme this is representing. ii. Assuming p(t) is rectangular with width 4µs state the bit rate for K = 16. iii. Sketch a labelled constellation diagram if p(t) is rectangular with height 1.5 and K = 8. iv. Using a technical discussion explain the effect of using a non-rectangular shape for p(t). [25 marks] Assessment criteria applies to individual and part of, questions. 30% - 40% Demonstrates little knowledge largely based on the material given and rote use of formula and information. Technique is mainly based on examples used in class sessions when performing calculations and presenting data, numerical errors present but not enough to obscure meaning. 40% - 50% Demonstrates basic knowledge largely based on the lecture notes. Technique lacking when performing calculations, interpretation of concepts and presenting data, numerical inaccuracy present. 50% - 60% Demonstrates knowledge based on taught material interpretation shows good knowledge of the subject. Appropriate technique used for calculations and presenting data, work contains some numerical inaccuracy. 60% - 70% Demonstrates some knowledge beyond taught material interpretation of source demonstrates good knowledge of the subject. Good technique used in calculations and presenting data, minor numerical inaccuracy present. +70% Demonstrates knowledge beyond taught material with good interpretation of taught and sourced material. Good technique used in calculations and presenting data, work contains insignificant numerical inaccuracy.